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Family of Generalized Integrals ${I}(a,b,p)=\int_0^{ab} \left( \left\{\frac{x}{a}\right\}-p\right) \left( \left\{\frac{x}{b}\right\}-p\right) \; dx$

Proof of Clairaut’s theorem in Terence Tao Analysis 2

Integral $\int_{0}^{\infty} \frac{\left(\frac{\pi x}{2}-\log (x)\right)^3}{\left(x^2+1\right)^2 \left(\log^2(x)+\frac{\pi ^2}{4}\right)} = \pi$ proof

Finding out the perimeter of the ellipse?

How to integrate Zoho CRM with Messagebird

Evaluating $\lim_{n\to\infty}\small\left(\frac{1}{\sqrt{n}\sqrt{n+1}}+\frac{1}{\sqrt{n}\sqrt{n+2}}+\cdots+\frac{1}{\sqrt{n}\sqrt{n+n}}\right)$

Define $I_n=\int_0^1\frac{x^n}{\sqrt{x^2+1}}dx$ for every $n\in\mathbb{N}$. Prove that $\lim_{n\to\infty}nI_n=\frac{1}{\sqrt 2}$.

Find a smooth function with prescribed moments

How to improve $\int_{0}^{\frac{\pi}{2}}x\left(\frac{\sin(nx)}{\sin(x)}\right)^{4}dx<\frac{\pi^{2}n^{2}}{4}$

Don't understand the Fundamental Theorem of Calculus

Examples of using Green's theorem to compute one-variable integrals?

Proof of Hölder inequality by differentiation

Abel summability of integrals

Infinite self-convolution for a function

Explanation for the integral of differential forms

How do I evaluate this definite integral?

Calculating a limit using dominated convergence theorem

New posts in integration

Help with change of variables in a double integral

Evaluating $\int_{0}^{2\pi}x^2\ln^2(1-\cos x)dx$

A difficult logarithmic integral and its relation to alternating Euler Sums

Family of Generalized Integrals ${I}(a,b,p)=\int_0^{ab} \left( \left\{\frac{x}{a}\right\}-p\right) \left( \left\{\frac{x}{b}\right\}-p\right) \; dx$

Proof of Clairaut’s theorem in Terence Tao Analysis 2

Integral $\int_{0}^{\infty} \frac{\left(\frac{\pi x}{2}-\log (x)\right)^3}{\left(x^2+1\right)^2 \left(\log^2(x)+\frac{\pi ^2}{4}\right)} = \pi$ proof

Finding out the perimeter of the ellipse?

How to integrate Zoho CRM with Messagebird

Evaluating $\lim_{n\to\infty}\small\left(\frac{1}{\sqrt{n}\sqrt{n+1}}+\frac{1}{\sqrt{n}\sqrt{n+2}}+\cdots+\frac{1}{\sqrt{n}\sqrt{n+n}}\right)$

Define $I_n=\int_0^1\frac{x^n}{\sqrt{x^2+1}}dx$ for every $n\in\mathbb{N}$. Prove that $\lim_{n\to\infty}nI_n=\frac{1}{\sqrt 2}$.

Find a smooth function with prescribed moments

How to improve $\int_{0}^{\frac{\pi}{2}}x\left(\frac{\sin(nx)}{\sin(x)}\right)^{4}dx<\frac{\pi^{2}n^{2}}{4}$

Don't understand the Fundamental Theorem of Calculus

Examples of using Green's theorem to compute one-variable integrals?

Proof of Hölder inequality by differentiation

Abel summability of integrals

Infinite self-convolution for a function

Explanation for the integral of differential forms

How do I evaluate this definite integral?

Calculating a limit using dominated convergence theorem