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- ...as a constant and thus you can pull the term associated with x outside the integral. </span>2 KB (290 words) - 10:17, 27 March 2013
- ...by simply replacing <math>j\omega</math> by s. In fact, the corresponding integral for s diverges for some values of s. -pm </span>2 KB (350 words) - 13:00, 27 March 2013
- a1. by using integral over function square E = 6 so P = 0582 B (120 words) - 06:35, 3 May 2013
- ...s are very different, we will see that for both cases, we measure the line integral of the density through the material. So if you get the projection through t8 KB (1,168 words) - 07:24, 26 February 2014
- ...ysical design of CT scanners and derive the differential equation and line integral needed for the inversion process using [[ECE637_tomographic_reconstruction_ ...density of the material, <math>\mu(x)</math> is always positive, so is its integral. The exponent is therefore always negative. This reiterates the notion that9 KB (1,390 words) - 07:24, 26 February 2014
- ...count how many annihilations occur along that detector and you get a line integral. So this is another technology where you the measurements are line integral6 KB (913 words) - 07:24, 26 February 2014
- Notice that, in an integral when changing from cartesian coordinates (dxdy) to polar coordinates <math> ...-x<sup>2</sup>=16 and 2xy=6 and 2xy=14.It'd be quite a simple task if the integral looked something like this:18 KB (2,894 words) - 12:17, 3 March 2015
- ...ore we must first perform a coordinate rotation in order to calculate this integral.6 KB (834 words) - 07:25, 26 February 2014
- We measure the projections as an integral of <math>f</math> along the <math>z</math> axis for every <math>r</math>. T ...eta</math> degrees counterclockwise from the <math>y</math> axis. The line integral along <math>z</math> is measured for every <math>r</math> at the given <mat6 KB (942 words) - 07:25, 26 February 2014
- ...same, as are the <math>x</math> and <math>r</math> axes, and in the above integral, <math>r</math> and <math>y</math> are just dummy variables. Next, taking t9 KB (1,485 words) - 12:30, 17 April 2014
- ...l to the current. The magnetic field is therefore also proportional to the integral of the voltage across the coil <br/> ...led by a voltage where the current through the coil is proportional to the integral of the voltage and the magnetic field of the coil is proportional to the cu27 KB (4,777 words) - 07:25, 26 February 2014
- ...i,\pi)</math> interval, only one term from the sequence is relevant to the integral, the <math>k=0</math> term. <br/>10 KB (1,726 words) - 07:26, 26 February 2014
- ...e operation of OUT instructions with and without a transparent latch as an integral part of the I/O block6 KB (936 words) - 07:32, 26 February 2014
- ...al cannot be used to evaluate ∫<math>_A</math>f(r)dr because the Riemann integral (RI) does not exist for some A∈''F''. For example, let <br/> ...nn integrable. This type of problem led to the development of the Lebesgue integral (LI). Integration in probability theory is assumed to be LI, because it can20 KB (3,448 words) - 12:11, 21 May 2014
- integral multiples of 200 kHz, and, possibly, some small spurs at some other frequen14 KB (2,228 words) - 12:03, 15 January 2014
- ...ee to use a table of integrals for any tricky integrals. (For example, the integral of exp(at)sin(bt) requires two ...out s^2 to get (1/(s^2)*(s^2-1)), also question says inverse transform by integral which is done in example 3. If you will integrate inverse transform of (1/(11 KB (2,033 words) - 14:02, 12 December 2013
- ...14a in class today. Split the integral up like the book suggests. For the integral4 KB (757 words) - 08:25, 16 October 2013
- Using integration by parts (proof), we see that this integral evaluates to <math>\sigma^2+\mu^2</math>. So, <br/>8 KB (1,474 words) - 12:12, 21 May 2014
- From [[User:Bell|Steve Bell]]: Jake, the n=1 term is the integral and that is a very easy integral to compute. You are right that the formula for the general8 KB (1,388 words) - 14:51, 29 October 2013
- ...ng on problem 2 of Lesson 31. There doesn't seem to be a way to solve the integral if you use formula (1b) with the answer from problem 1. Any tips? ...h of sinc function integrals which have to be evaluated with the Dirichlet Integral. I can use Table 11.10 relationship #10 and get the answer without chuggin6 KB (1,130 words) - 18:15, 5 November 2013
- > integral of the function will be the same. 2+1+1+ a sum of squares = (1/pi) integral of |f|^211 KB (1,959 words) - 17:57, 10 November 2013
- ...a double root at -y^2. However, it appears that the solution should be the integral of this based on the y^3/3 in the back of the book. Any advice? ...plit it into 4 integrals (0 to 1/4, 1/4 to 1/2, etc.). The first and last integral are zero but you can get an f(x) for the middle two from the graph. It's s6 KB (1,102 words) - 19:16, 19 November 2013
- [[Category:integral]]5 KB (942 words) - 18:13, 26 February 2015
- ...is neither so no simplification there. Integration by parts yields another integral that needs integration by parts and it looks never ending. So I am thinking ...just move it to the other side of the equation and solve for it, as if the integral was a variable. A(w) should be 2/[pi(w^2+1)] and B(w) is 0.5 KB (978 words) - 17:36, 3 December 2013
- ...It provides the foundation for key management and digital signatures, both integral parts of any cryptosystem. Below is a pictorial representation illustrating19 KB (3,051 words) - 22:23, 4 December 2013
- The unique factorization property can be formulated in any integral domain. Consider the ring Z[i] of Gaussian integers. Here i=√(-1), and th12 KB (2,127 words) - 17:06, 27 April 2014
- Now let us look at an example to understand how we can write this integral in terms of <math>Prob \left( \omega_1 \vert x\right)</math> and <math>Pro In most cases solving either integral is intractable because these could be integrals in large dimensions. Theref13 KB (2,062 words) - 10:45, 22 January 2015
- ** Might want to mention why solving for the integral in the expression for probability of error is intractable.2 KB (257 words) - 08:51, 11 May 2014
- * In Eq. (3.10), it might help to remark that the integral equals 1 because the probabillity distribution integrates to 1.2 KB (410 words) - 15:54, 30 April 2014
- ...ind of surprised that there were no problems which asked to compute a real integral by taking a detour through the complex plane. There was also no problem whi .... I tried using the Residue Theorem but found myself unable to compute the integral. I ended up computing the first few terms of the series expansion of the de2 KB (363 words) - 14:54, 25 August 2014
- ...function <math> \phi(x/h) </math>. <math> \phi </math> must have a finite integral.9 KB (1,604 words) - 10:54, 22 January 2015
- ...at our disposal for finding whether a series converges or not, namely, the integral test, the comparison and limit comparison tests, alternating series test, t9 KB (1,632 words) - 18:19, 27 February 2015
- Evaluate the integral <math>\displaystyle\int_0^\infty\frac {\sqrt x}{x^2+1}dx</math> using techn By the residue theorem, for <math>R > 1</math>, the integral is also equal to the residue at <math>i</math> (there are two simple poles10 KB (1,792 words) - 05:43, 10 August 2014
- *On problem 2 (contour integral problem <br><math>\int_0^\infty \frac{\cos(8x)}{x^2+1} \, dx</math><br>if I730 B (134 words) - 06:50, 5 August 2014
- ...hould mention of use of the translation property used to quickly solve the integral. Overall, this slecture is cleanly organized. Good job!5 KB (843 words) - 05:30, 15 October 2014
- ...r. In the example it would be good to mention the sifting property for the integral of a delta. I like how the reasoning is explained for the work and why the3 KB (568 words) - 05:34, 15 October 2014
- ...easure projections through an object with density. A Radon Transform is an integral that allows the calculation of the projections of an object as it is scanne ...perpendicular to the <math>r</math> axis. This implies that the projection integral is <br />5 KB (788 words) - 19:25, 9 February 2015
- =Extracting the Line Integral for Convolution Back Projection= ...|convolution back projection]] can be used to produce slices for each line integral which will stack to become a 3D representation of the patient's body.7 KB (1,072 words) - 19:25, 9 February 2015
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- [[Category:integral]] ...nd-inline-policy: -moz-initial; font-size: 110%;" colspan="2" | Particular Integral, componant <math> x^4 - a^4</math>13 KB (2,180 words) - 18:02, 26 February 2015
- e) Calculate an expression for the integral of the density, <math> \int_{0}^{T} \mu dx </math>, in terms of <math>\lamb3 KB (524 words) - 12:53, 7 December 2015
- Using the Fourier integral:499 B (69 words) - 00:24, 12 July 2016
- ...em] or [https://en.wikipedia.org/wiki/Cauchy%27s_integral_formula Cauchy's integral formula] to analyze the values of the DFT based on its Z-transform.6 KB (931 words) - 23:40, 23 April 2017
- d) Calculate an expression for the integral of the density, <math> \int_0^T u(x)dx</math>, in terms of the measured val3 KB (566 words) - 16:39, 18 May 2017
- d) So the integral of the density, <math>\int^T_0\mu(x)dx </math> can be written as3 KB (529 words) - 16:42, 18 May 2017
- ...hing the variables to make the same variable on the same side, in order to integral on both sides and solve out the function (solution) The standard form of di10 KB (1,764 words) - 14:31, 17 November 2017
- ...for <math>\frac{dy}{dt}=f(t)</math>. This is the same thing as finding the integral of <math>f(t)</math> with respect to <math>t</math>.5 KB (852 words) - 22:39, 16 November 2017
- ...he conservative vector field is path independent, thus a circulation (line integral over a closed path) is zero.9 KB (1,373 words) - 14:16, 19 February 2018
- The evaluation of the previous integral has terms for <math>i_{bs}' = 0</math> (lower bound evaluation) that must n6 KB (991 words) - 18:28, 26 January 2018
- ...ork done by the electromagnetic force on the mechanical system is the line integral of the force with the differential displacement. (Negation arises from the ...rrent. The mechanical energy transferred to the coupling field is the line integral of electromagnetic force over displacement (work done ''by'' the coupling f7 KB (1,270 words) - 14:25, 12 February 2018
- ...he conservative vector field is path independent, thus a circulation (line integral over a closed path) is zero.4 KB (667 words) - 14:50, 19 February 2018
- The evaluation of the previous integral has terms for <math>i_{1}' = 0</math> (lower bound evaluation) that must no The evaluation of the previous integral has terms for <math>i_{2}' = 0</math> (lower bound evaluation) that must no5 KB (806 words) - 15:29, 19 February 2018
- ...he 1-D equations we have seen this semester, with the addition of an extra integral/summation, and an additional independent variable. They are as follows:2 KB (402 words) - 20:47, 1 December 2018
- ...io, Φ, (sqrt(5)+1)/2. This number appears in many contexts and will be an integral part of Penrose tilings with these two shapes. First, let us look at these8 KB (1,327 words) - 17:44, 2 December 2018
- 3. Calculate an expression for <math>\hat{P}_n</math>, an estimate of the integral intensity in terms of <math>\lambda_n</math>, <math>\lambda_n^b</math>, and3 KB (575 words) - 03:07, 26 April 2020
- In continuous time, a convolution is defined by the following integral:7 KB (1,006 words) - 22:10, 22 December 2019
- ...r transform usually eliminates the bounds and instead utilizes an improper integral:<br /><br />12 KB (2,051 words) - 14:20, 5 December 2020
- ...ase "u") represent a portion of our integral. For example, let's take this integral: ...h>. We can then proceed to use this as a substitution for dx, changing our integral to <math> \int {sin{(u)} du}</math>, which is much easier to compute.1 KB (207 words) - 17:53, 4 December 2020
- ...get an integral that is easier to work with. A simple example would be an integral such as: ...a function, focusing on the cosine factor of the integrand. By writing the integral as a function, we can change the expression to:4 KB (640 words) - 20:41, 30 November 2020
- The integral evaluates to <math> \frac{L}{2}</math>, so <math> A = (\frac{2}{L})^{\frac{ ...ns of this result is the variable <math> n </math>; as it can only take on integral values, the energy of the particle is '''quantized''', restricted to discre11 KB (1,781 words) - 20:34, 6 December 2020
- # Cauchy’s Integral Theorem ==== Cauchy’s Integral Theorem ====8 KB (1,390 words) - 16:12, 6 December 2020
- A simple example would be an integral such as: ...a function, focusing on the cosine factor of the integrand. By writing the integral as a function, we can change the expression to:3 KB (578 words) - 01:34, 2 December 2020
- ...r the integral sign. This method of integration is also known as "Leibniz' Integral Rule". ...model. His technique to solve integrals by using differentiation under the integral sign helps to find the derivative on the nth order of the product of two fu1 KB (205 words) - 03:06, 3 December 2020
- ...t this function can be solved easily if we using differentiation under the integral sign. Therefore, let's define a more basic function:2 KB (408 words) - 12:42, 3 December 2020
- ...e can set F(a) equal to an easier integral and differentiate it to get the integral in the problem. For example, let's take the integral in the video:3 KB (574 words) - 22:24, 2 December 2020
- ...t this function can be solved easily if we using differentiation under the integral sign. Therefore, let's define a more basic function:2 KB (408 words) - 12:35, 3 December 2020
- ...''V'', we can use Feynman's rule to manipulate the gradient and potential integral so that we can solve the solution in an easier way.2 KB (388 words) - 18:22, 4 December 2020
- When used in different types of integrals, Feynman's integral can simplify mathematicians' and students' lives. We can use this technique When given a definite integral such as,889 B (141 words) - 01:36, 5 December 2020
- Feynman's integral when used in different types of integrals can simplify mathematicians' and166 B (21 words) - 17:46, 4 December 2020
- When used in different integrals, Feynman's integral can simplify mathematicians' and students' lives. We can use this technique When given a definite integral such as,3 KB (525 words) - 03:12, 5 December 2020
- ...''V'', we can use Feynman's rule to manipulate the gradient and potential integral so that we can solve the solution in an easier way.2 KB (403 words) - 18:01, 5 December 2020
- ...single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute ...ve seen over these past few slides, there are many ways to apply Feynman's integral technique, both mathematically and towards other subjects. Although this in2 KB (307 words) - 21:13, 5 December 2020
- ...>i</sub>(t) and t ∈ [-1,1] using each γ<sub>i</sub> path. Finally, the integral can be written as: ...the amount of space under the Riemann Surface, just like any “regular” integral.2 KB (400 words) - 00:02, 6 December 2020
- <small>''note: <math>\int[f(X;θ)]dx</math> simplifies out to one because the integral of a probability function is always 1.''</small><br />2 KB (351 words) - 23:13, 6 December 2020
- ...eorem could apply to non-integer powers so by representing this area as an integral of the binomial theorem's expansion he had an infinite series which converg18 KB (2,815 words) - 11:22, 8 December 2022
