Ask Question
Questions about the evaluation of specific definite integrals.
18,376 questions 3- Bountied 3
- Unanswered
- Frequent
- Score
- Unanswered (my tags)
Need help plugging in bounds in a u-substitution
This is a really basic question but I'm just a little confused. I have this integral: $$\int_{0}^{2\pi}\cos^3tdt$$ I solved it by doing a u-sub: $$\int_{0}^{2\pi}\cos t(1-\sin^2t)dt$$ Let $u=\sin t$, ... calculus integration definite-integrals- 598
Is there any method other than Feynman’s Integration Technique to find $ \int_{0}^{\frac{\pi}{2}} \ln \left(a \cos ^{2} x+b \sin ^{2} x+c\right) d x?$
We are going to find the formula, by Feynman’s Integration Technique, for $$\int_{0}^{\frac{\pi}{2}} \ln \left(a \cos ^{2} x+b \sin ^{2} x+c\right) d x,$$ where $a+c$ $\textrm{ and }$ $b+c$ are ... calculus integration definite-integrals- 5,342
Asymptotics of a two dimensional integral
I am working on the following integral $\int_0^1d\epsilon\int_{-\epsilon}^\epsilon dt (\sqrt{1-(\rho+t)^2}-\sqrt{1-\rho^2})e^{-N t^2},$ where $\rho=1-\epsilon$, $N\rightarrow \infty$. The problem is ... integration definite-integrals asymptotics approximate-integration- 73
Analytical solution of an integral involving gaussian
I was wondering if there is any analytical solution to the following integral: $$\int_L^U\frac{e^{-\frac{(x-a)^2}{2\sigma^2}}}{x} dx$$ with $\sigma, L, U>0$. integration definite-integrals- 514
Integral result contains one term is infinite large and one term is infinite small.
I am trying to integrate this function from $0$ to $f$. $ \int_0^f\dfrac{p\cdot\left(\mathrm{e}^{-\frac{\ln\left(r\right)\,x}{\left(r-1\right)t}}-\mathrm{e}^{-\frac{r\ln\left(r\right)\,x}{\left(r-1\... calculus integration definite-integrals- 21
Asymptotics of an integral with singular derivation
I want to evalute the leading order term of the following integral as a series of $1/N$ and $\epsilon$, $\int_{-\epsilon}^\epsilon dt (\sqrt{1-(\rho+t)^2}-\sqrt{1-\rho^2})e^{-N t^2}$, where $\rho=1-\... integration definite-integrals asymptotics approximation- 73
Integral of product of modified Bessel functions: $ \int_0^{\infty} r e^{- a r^2} I_k (b r^2) I_{2k-n} (c r) d r $
The following integral appeared in my research recently. $$ \int_0^{\infty} r e^{- a r^2} I_k (b r^2) I_{2k-n} (c r) d r , \tag{*} $$ where $c \geq 0$, $a > b \geq 0$, and $k , n \in \mathbb{Z}$. ... integration definite-integrals improper-integrals special-functions bessel-functions- 559
von Mises distribution and related integral
Recently, I have known about von Mises distribution, which is given by $$f_{\text{vM}}(\varphi;\kappa,\mu)=\frac{1}{2\pi I_0(\kappa)}\exp\left\lbrace\kappa\cos\left(\varphi-\mu\right)\right\rbrace,\... probability probability-distributions definite-integrals- 347
Evaluate $\int_{-\infty}^\infty e^{i(\omega-\omega_0)t}\mathrm\;{dt}$
Evaluate $$\int_{-\infty}^\infty e^{i(\omega-\omega_0)t}\mathrm\;{dt}$$ This is an integration from a textbook chapter discussing wave involving Fourier transform, which try to deal with dispersion. ... integration definite-integrals complex-numbers fourier-transform- 1
Prove close form $\int_a^1 \frac{x}{\sqrt{x^2-a^2}}\ln\frac{\sqrt{1+x}+\sqrt{1-x}}{\sqrt{1+x}-\sqrt{1-x}}dx=\frac{\pi}{2}(1-a)$
I found this integral in a textbook (stated without proof), $$J(a)=\int_a^1 \frac{x}{\sqrt{x^2-a^2}}\ln\frac{\sqrt{1+x}+\sqrt{1-x}}{\sqrt{1+x}-\sqrt{1-x}}dx=\frac{\pi}{2}(1-a)$$ with $0\le\,a\le\,1$. ... calculus integration definite-integrals- 41
Arc length vs Surface of revolution.
I don't understand why these two problems are solved differently here the first one $fig(1)$ and 2nd one $fig(2)$. Why did we take the limit $\displaystyle \lim_{r\to0^+}\int_r^\pi \sqrt{2-2cost}\... calculus integration algebra-precalculus definite-integrals applications- 59
How to find $\int_{0}^{\pi} \ln (b \cos x+c)$ without using Feynman’s integration technique?
I shall find the integral by Feynman’s Technique Integration on a particular integral $\displaystyle I(a)=\int_{0}^{\pi} \ln (a \cos x+1) d x,\tag*{} $ where $-1\leq a \leq 1.$ $\displaystyle \begin{... calculus integration definite-integrals- 5,342
Find the length $L$ of the catenary
$C$: $y = \cosh(x)$, $\,\log(2) \leq x \leq \log(3)$. I did arrive at the problem until $\sinh b$, but I don't know how to continue. Should it be $\sinh(\log(3))$? calculus integration definite-integrals hyperbolic-functions arc-lengthDefinite integral $ \int _{0}^{\infty } x\cdotp \tanh( 2x) \cdotp \ln(\coth x)\mathrm{d} x$
I want to show that $\displaystyle \int\limits _{0}^{\infty } x\cdotp \tanh( 2x) \cdotp \ln(\coth x)\mathrm{d} x=\frac{\pi ^{2} \cdotp \ln( 2)}{2^{4}}\tag*{}$ I tried integration by parts, Feynman ... calculus integration definite-integrals improper-integrals hyperbolic-functions- 195
Find the area of the region inside the cardioid r = 1 ( 1 - sinθ ) and outside the circle r = 1 [closed]
I don't know how to draw the graph of the cardioid integration definite-integrals area polar-coordinates- 1
15 30 50 per page12345…1226 Next
