New posts in integration

Trouble solving $\int\sqrt{1-x^2} \, dx$

calculus integration indefinite-integrals

Computing the integral $\int \exp(ix^2) dx$

calculus integration gaussian-integral

Find the value of : $\lim_{n\to\infty}[(n+1)\int_{0}^{1}x^{n}\ln(1+x)dx]$.

integration definite-integrals

Explaining $\int_{-1}^1\frac{1}{1+x^2}\,dx = \frac{\pi}{2}$.

calculus integration

Calculating sum of converging series $\sum_{n=1}^{\infty}\frac{1-n}{9n^3-n}$

integration sequences-and-series

$\int_0^1\frac{\ln x\ln^2(1-x^2)}{\sqrt{1-x^2}}dx=\frac{\pi}{2}\zeta(3)-2\pi\ln^32$

integration sequences-and-series definite-integrals logarithms riemann-zeta

Prove $\int_{\mathbb{R}^n}e^{-\max\{|x_1|,\ldots,|x_n|\}}dx=2^nn!$

calculus integration

Prove that $\int_E |f_n-f|\to0 \iff \lim\limits_{n\to\infty}\int_E|f_n|=\int_E|f|.$

real-analysis integration measure-theory convergence-divergence solution-verification

Find $\int\frac1x\sqrt\frac{1-x}{1+x}\ dx$

integration

How to write an integral as a limit?

calculus integration

Doesn't the constant matter in $\int\frac{1}{x}dx=\ln(kx)+C$ instead of writing $\ln(x)+C$?

calculus integration indefinite-integrals

How to find double integral borders knowing the object's limitations?

integration analysis

How does integration by parts lead to $\int f'(x)g(x)dx = -\int g'(x)f(x)dx$

integration derivatives

Evaluate the volume bounded by $z=1-x^2-y^2$ and $z=1-y.$

integration analysis multivariable-calculus multiple-integral

Integral $\int_0^\infty \log \frac{1+x^3}{x^3} \frac{x \,dx}{1+x^3}=\frac{\pi}{\sqrt 3}\log 3-\frac{\pi^2}{9}$

calculus real-analysis integration complex-analysis definite-integrals

Suggestion for Computing an Integral

calculus integration analysis definite-integrals

A continuous function defined on an interval can have a mean value. What about a median?

integration functions median means

For any given function $f\colon [0,1]\to\Bbb R$, what is $\int_0^1\frac{f(x)}{f(x)+f(1-x)}dx$?

calculus real-analysis integration definite-integrals closed-form

A function that is bounded and measurable but not Lebesgue integrable

real-analysis integration measure-theory lebesgue-measure examples-counterexamples

A uniformly continuous function whose integral $\int_0^\infty f(x)dx$ exists converges to zero

real-analysis integration uniform-continuity