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- ...a closed interval [a,b]. Let F be the function for all x in [a,b] by F(x)=Integral from a to x of f(t) dt. Then F is continuous on [a,b] and differental on th ...val [a, b]. Let F be an antiderivative of f, for all x in [a, b], Then the integral from a to b of f(x) dx equals F(a)-F(b).643 B (138 words) - 15:17, 1 September 2008
- The fundamental theorem of calculus states that the integral of a function f over the interval [a, b] can be calculated by finding an an integral from a to b of f(x) dx = F(b) - F(a)307 B (59 words) - 06:09, 8 September 2008
- is an integral domain, and hence has no zero-divisors) nor a unit.585 B (86 words) - 09:51, 21 March 2013
- Prove that there is no integral domain with exactly six elements ...here to begin on this problem. I do not know how to prove that there is no integral domain with six elements. A little help would be nice. Thanks3 KB (460 words) - 09:45, 21 March 2013
- ...another ring they have the same multiplication, addition, and zero, a non-integral domain can't be contained in a field.495 B (81 words) - 17:09, 29 October 2008
- ...sift' out''', hence the name, '''a particular value of the function in the integral''' at an exact instant in time. Doesn't the function do that by itself outside of the integral anyways?2 KB (305 words) - 11:17, 24 March 2008
- ...m and therefore it is a variable and not a constant. So when you write the integral it is of the form <math>\int{x e^x}dx</math> and not <math>\int{c e^x}dx </ ...then at pi/2 it would be division by zero. I also don't understand why the integral for the inverse transform is taken of -pi to pi when the solution key previ4 KB (683 words) - 21:46, 6 April 2008
- <math>E(u)=\int _{0} ^{1} ||\nabla u||^2 dx</math> (3-13) Dirichlet integral8 KB (1,337 words) - 08:44, 17 January 2013
- The function is not time invariant because the integral will evaluate from negative infinity to twice the current time. This will3 KB (499 words) - 17:51, 16 June 2008
- I used the integral y(t) = <math>\int_{-\infty}^\infty h(\tau)x(t-\tau)\,d\tau</math> for simpl1 KB (286 words) - 23:53, 17 June 2008
- The integral of the magnitude squared will always be positive for an odd signal.4 KB (739 words) - 20:48, 30 July 2008
- We start with part B by noticing that the integral of the delta function is a step function. So the energy over an infinite interval is just the integral of the step function <math>u(t + 2) - u(t - 2)</math>1 KB (210 words) - 19:53, 2 July 2008
- ...</math> so <math>g(x) \in AC[0,1]</math> by the absolute continuity of the integral.905 B (182 words) - 11:43, 10 July 2008
- ...|</math>, so two applications of MCT allow us to pass the limit inside the integral, yielding the result. <math>\square</math>.4 KB (748 words) - 11:54, 10 July 2008
- The last but two inequality is due to the integral form of Jensen's inequality.872 B (174 words) - 11:15, 10 July 2008
- .../math>, which we are afforded by the absolute continuity of the indefinite integral of <math>|g|^q</math>. By Egorov, we may select closed <math>F \subset X,1 KB (219 words) - 17:00, 10 July 2008
- ...sect. 4, Corollary 15 gives f is absolutely continuous iff its the indef. integral of its derivative.463 B (68 words) - 10:54, 16 July 2008
- *<span style="color:green"> Be careful! The stuff inside the integral should always be positive. You are integrating "t", which is sometimes posi6 KB (975 words) - 15:35, 25 February 2015
- Computing the integral:803 B (142 words) - 07:55, 22 June 2009
- ...c{\cos x}{\sqrt{\sin x}} \text{ is finite a.e. on a bounded domain, so the integral exists}</math>1 KB (201 words) - 18:10, 5 July 2009
- Now, we need to pull the limit inside the integral, so we proceed as follows: ...w, by the Dominating Convergence Theorem, we can pull the limit inside the integral.2 KB (437 words) - 11:01, 6 July 2009
- ...0}</math> is constant over <math>\tau</math> it can be factored out of the integral1 KB (240 words) - 16:58, 8 July 2009
- Because the linearity of the integral.378 B (68 words) - 21:45, 8 July 2009
- Letting <math>\tau</math>=t-<math>t_{0}</math> in the integral, and noticing that the new variable <math>\tau</math> will also range over<1 KB (200 words) - 03:44, 9 July 2009
- Letting <math>\tau</math> = t - <math>t_0</math> in the new integral and noting that the new variable <math>\tau</math> will1 KB (266 words) - 03:10, 23 July 2009
- Now, since f and g are both <math>L^{1}</math>, this integral exists, so by Fubini's Theorem, we may rewrite it as: ...again (since all of these are equalities, we don't need to check that the integral exists, since it's automatic), to get:1 KB (264 words) - 05:57, 11 June 2013
- I forgot to justify why the integral exists in the first place. Well, since <math>f\in C_c^{\infty}(R^n)</math>2 KB (374 words) - 05:56, 11 June 2013
- The integral is taken over the interval of T. The sum is taken from -infinity to infini137 B (25 words) - 16:54, 27 July 2009
- The integral is taken over the interval T. The sum is taken from <math>-\inf to \inf</m138 B (27 words) - 16:58, 27 July 2009
- We can pass this limit through the integral since <math>\hat{f}</math> is dominated by <math>f\in L^1</math>2 KB (315 words) - 05:55, 11 June 2013
- ...nn integrable, hence the Lebesgue integral will be the same as the Riemman integral.2 KB (282 words) - 05:53, 11 June 2013
- <math>f = f*f = \int_{\mathbb{R}} f(x-y)f(y)dy = 0 </math> because the integral of something that is zero a.e. is zero.1 KB (168 words) - 05:53, 11 June 2013
- Proof. First we find the integral by using substition and the result of 7.3:4 KB (657 words) - 05:53, 11 June 2013
- <i>Solution:</i> Following the hint, we consider the integral <math>\phi ( \xi ) = \frac{1}{\sqrt{4\pi}}\int_{{\mathbb R}} \cos (2\pi x \ ...ect to <math>\xi</math> (in the sense that we can differentiate inside the integral).<br>4 KB (797 words) - 05:54, 11 June 2013
- ...aplace transform $X(s)$ of a given $x(t)$ depends on whether the transform integral converges ...of a sinusoid which is bounded and has no effect on the convergence of the integral).3 KB (494 words) - 04:22, 30 July 2009
- c[n] = 1/T * integral{q(t) * exp(-j*2*pi*n/T*t) dt} c[n] = 1/T * integral{T * SUM{ d(t - k*T) } * exp(-j*2*pi*n/T*t) dt}1 KB (196 words) - 04:17, 30 July 2009
- Since priors are independent of ''x'', we can take priors out of the integral. Let the integral part in eq.(2.8) be the Chernoff <span class="texhtml">β</span>-coefficien17 KB (2,590 words) - 10:45, 22 January 2015
- in this case the integral is around a counter-clockwise clothed path encircling the origin of the com2 KB (252 words) - 06:55, 16 September 2013
- The trick to step two is to realize that taking the integral of a weighted sum of impulses is simply the sum of the weights. The result8 KB (1,452 words) - 06:49, 16 September 2013
- ...nderpinnings of real numbers, or even being concerned with knowing how the integral formula is derived. A good student who really wants to understand the mater ...fferent phenomena. There are exponential functions, logarithmic functions, integral functions, differential operators, matrix functions, hyperbolic functions,27 KB (4,384 words) - 17:47, 26 October 2009
- ...ically--some will be indifferent, and will allow you to use software or an integral table, but others might be less merciful. In any case, this is not a class6 KB (1,067 words) - 18:07, 26 October 2009
- ...nity, of the integral showing that the integrand approaches 0 and thus the integral goes to 0?--[[User:Apdelanc|Adrian Delancy]]3 KB (578 words) - 09:12, 7 October 2009
- Evaluate the integral to get:3 KB (613 words) - 15:22, 11 October 2009
- Professor Bell, You showed in class that we can't show that the integral around the curved portion for problem VI.12.2 goes to zero using the basic ...is integral must be the negative of the integral found in (I). To do this integral, let <math>z=t\exp(i\frac{\pi}{8})</math>. The real part is what we are lo2 KB (359 words) - 05:56, 21 October 2009
- ..., 0<=t<=R), you integrate <math>1/(t^2+a^2)</math> from 0 to infinity. The integral of <math>1/(t^2+a^2)</math> is <math>arctan(t/a)/a</math>. Next show that the integral of 'circle portion' is 0.2 KB (290 words) - 06:06, 30 October 2009
- ...nitial; -moz-background-inline-policy: -moz-initial;" colspan="2" | Vector Integral formulas13 KB (1,854 words) - 11:58, 24 February 2015
- *Also, a close look at the above integral, shows that it is simply a convolution of the mother wavelet and the signal10 KB (1,646 words) - 11:26, 18 March 2013
- ...and use the substitution <math>exp(i\theta)=z</math>. This expresses the integral in the complex plane along the unit circle in the counterclockwise directio4 KB (631 words) - 11:08, 14 December 2009
- ...owing that <math>{f}</math> is analytic on <math>\Omega</math> we know the integral over <math>\gamma</math> is zero. Letting <math>\omega\in\gamma</math> we722 B (130 words) - 11:44, 8 February 2010
- ...ic package: http://stat.ethz.ch/CRAN/web/packages/elliptic/index.html, for integral with complex numbers.4 KB (596 words) - 13:17, 12 November 2010
