List questions from definite-integrals

Published on 14 Apr 2026 - 21:25

158

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Find $\int_{-\pi/2}^{\pi/2} \frac{\cos^3 x}{e^x+1} dx$

Published on 15 Apr 2026 - 11:19

489

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Assume $f \in R[a, b]$. Show that if $c \in [a, b]$ then $\int_a^c f(x)dx + \int_c^b f(x)dx = \int_a^b f(x)dx$

Published on 12 May 2018 - 13:12

68

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Integral word problem check. Is this right?

Published on 13 Apr 2026 - 21:04

65

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Let $I=\int_{-\pi}^{\pi}\dfrac{sin^2x}{1+a^x}dx,a>0$.Find the value of $I$

Published on 14 Apr 2026 - 12:27

81

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Finite Difference Equation From a Non-Linear Equation

Published on 09 Apr 2026 - 4:27

444

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Evaluating $\lim_{n\rightarrow\infty} \int_{0}^{\pi} \frac {\sin x}{1+ \cos^2 (nx)} dx$

Published on 15 Apr 2026 - 8:06

2.1k

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Showing $\Phi(x)=\int_0^x (x-t)f(t)\,dt$ is twice differentiable and finding $\Phi''(x)$

Published on 13 May 2018 - 14:08

336

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For what values of $\alpha$, does this integral converge?

Published on 14 Apr 2026 - 12:22

841

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definite integral with limits (both bounds become negative infinity)

Published on 11 Apr 2026 - 21:04

335

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Assume that $f$ is Riemann integrable over $[a, b]$. Show that $|f| \in R[a,b]$

Published on 13 Apr 2026 - 18:12

87

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Is this Evaluation of definite Integral correct?

Published on 14 Apr 2026 - 0:38

221

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Differential geometry - Calculating length of a curve

Published on 15 Apr 2026 - 4:54

109

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what is difference between $\int_{0}^{1+x^3}\sqrt{t}$ and $\int_{0}^{x^3}\sqrt{1+t}$ and $\int_{0}^{x}\sqrt{1+t^3}$?

Published on 13 May 2018 - 20:41

106

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What is the closed form solution for this integral or series?

Published on 14 Apr 2026 - 20:43

List Question

Approximation of an elliptic integral

Find $\int_{-\pi/2}^{\pi/2} \frac{\cos^3 x}{e^x+1} dx$

Assume $f \in R[a, b]$. Show that if $c \in [a, b]$ then $\int_a^c f(x)dx + \int_c^b f(x)dx = \int_a^b f(x)dx$

Integral word problem check. Is this right?

Let $I=\int_{-\pi}^{\pi}\dfrac{sin^2x}{1+a^x}dx,a>0$.Find the value of $I$

Finite Difference Equation From a Non-Linear Equation

Evaluating $\lim_{n\rightarrow\infty} \int_{0}^{\pi} \frac {\sin x}{1+ \cos^2 (nx)} dx$

Showing $\Phi(x)=\int_0^x (x-t)f(t)\,dt$ is twice differentiable and finding $\Phi''(x)$

For what values of $\alpha$, does this integral converge?

definite integral with limits (both bounds become negative infinity)

Assume that $f$ is Riemann integrable over $[a, b]$. Show that $|f| \in R[a,b]$

Is this Evaluation of definite Integral correct?

Differential geometry - Calculating length of a curve

what is difference between $\int_{0}^{1+x^3}\sqrt{t}$ and $\int_{0}^{x^3}\sqrt{1+t}$ and $\int_{0}^{x}\sqrt{1+t^3}$?

What is the closed form solution for this integral or series?

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