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

Prove two series are equal

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?

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

Computing $ \int_0^{\infty} \frac{ \sqrt [3] {x+1}-\sqrt [3] {x}}{\sqrt{x}} \mathrm dx$

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

Calculus - can I do this?

How find limit $\displaystyle \lim_{n\to\infty}n\left(1-\tfrac{\ln n}{n}\right)^n$

Derivative of exponential function proof

Optimization of the area of a cross inscribed in a circle

Limit of a sequence with indeterminate form

Evaluate $\int_0^\infty \frac{dx}{(x+\sqrt{1+x^2})^2}$

how to evaluate $\lim_{x\to0} (x^2)/(e^x-1) $ without L'Hospital

Evaluate $\lim_{n\to \infty} \sum_{r=1}^n \frac {1}{2^r}\tan \left(\frac {1}{2^r}\right)$

New posts in calculus

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

Maclaurin expansion of $\arctan(x)/(1 − x).$

Summation Formula for Tangent/Secant Numbers

Prove that $e$ is transcendental.

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

Prove two series are equal

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?

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

Computing $ \int_0^{\infty} \frac{ \sqrt [3] {x+1}-\sqrt [3] {x}}{\sqrt{x}} \mathrm dx$

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

Calculus - can I do this?

How find limit $\displaystyle \lim_{n\to\infty}n\left(1-\tfrac{\ln n}{n}\right)^n$

Derivative of exponential function proof

Optimization of the area of a cross inscribed in a circle

Limit of a sequence with indeterminate form

Evaluate $\int_0^\infty \frac{dx}{(x+\sqrt{1+x^2})^2}$

how to evaluate $\lim_{x\to0} (x^2)/(e^x-1) $ without L'Hospital

Evaluate $\lim_{n\to \infty} \sum_{r=1}^n \frac {1}{2^r}\tan \left(\frac {1}{2^r}\right)$