Question

Compute $\lim\limits_{n \to \infty} n\sum\limits_{k=1}^n(f(k/n) - f((k-1)/n))\int_{(k-1)/n}^{k/n}f(t)dt$

score 403 · Answer 1 · 2026-04-10 10:25:17

403

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Compute $\lim\limits_{n \to \infty} n\sum\limits_{k=1}^n(f(k/n) - f((k-1)/n))\int_{(k-1)/n}^{k/n}f(t)dt$

Published on 10 Apr 2026 - 10:25

score 70 · Answer 2 · 2026-04-09 19:42:17

70

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Integral of function from $0$ to $\pi$ using $\sin x=t$ substitution

Published on 09 Apr 2026 - 19:42

score 146 · Answer 3 · 2026-04-10 10:25:21

146

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How to figure out this definite integral

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score 158 · Answer 4 · 2026-04-09 02:00:46

158

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How to calculate $\iint_{\mathbb{R}^2} \exp\left(-x^2-y^2+ixy-ix-iy\right)\,dx\,dy$?

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score 205 · Answer 5 · 2026-04-12 01:49:32

205

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Integration of an exponential function over a triangle. Numerically stable approximation to the infinite sum?

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score 217 · Answer 6 · 2018-01-26 15:14:44

217

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How to solve the integral $\int \frac{4+12x}{({1-2x-3x^2})^\frac{2}{3}}\,dx$

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score 72 · Answer 7 · 2026-04-09 02:43:47

72

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$\int _0^ax\left(1-\frac{x}{a}\right)dx\:$ using Riemann Sums

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score 133 · Answer 8 · 2026-04-09 05:32:53

133

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Partial Fraction problem solution deviates from the Rule

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score 800 · Answer 9 · 2018-01-26 17:04:53

800

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Integration by parts: $\int(x+1)^2\ln(3x)\,dx$

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score 60 · Answer 10 · 2026-04-12 15:01:41

60

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How to integrate $\int\frac{\sin(kx)}{e^x}dx?$

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score 109 · Answer 11 · 2026-04-09 17:58:52

109

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Intuitive understanding of integrating a cumulative distribution function

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score 175 · Answer 12 · 2026-04-08 23:47:58

175

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Show that $\int_0^1\frac{\ln(x)^n}{x-1}dx=(-1)^{n+1}n!\zeta(n+1)$, for $n\geq 1$

Published on 08 Apr 2026 - 23:47

score 91 · Answer 13 · 2026-03-24 22:08:46

91

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Compute $\int\frac{x^2}{\tan{x}-x}dx$ for $x \in (0, \frac{\pi}{2})$

Published on 24 Mar 2026 - 22:08

score 1.4k · Answer 14 · 2026-03-25 07:51:27

1.4k

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Necessary condition for improper integral of odd and even functions to converge

Published on 25 Mar 2026 - 7:51

score 5.6k · Answer 15 · 2026-04-09 00:09:12

5.6k

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Find an appropriate trigonometric substitution of the form x=f(t) to simplify the integral

Published on 09 Apr 2026 - 0:09

List Question

Compute $\lim\limits_{n \to \infty} n\sum\limits_{k=1}^n(f(k/n) - f((k-1)/n))\int_{(k-1)/n}^{k/n}f(t)dt$

Integral of function from $0$ to $\pi$ using $\sin x=t$ substitution

How to figure out this definite integral

How to calculate $\iint_{\mathbb{R}^2} \exp\left(-x^2-y^2+ixy-ix-iy\right)\,dx\,dy$?

Integration of an exponential function over a triangle. Numerically stable approximation to the infinite sum?

How to solve the integral $\int \frac{4+12x}{({1-2x-3x^2})^\frac{2}{3}}\,dx$

$\int _0^ax\left(1-\frac{x}{a}\right)dx\:$ using Riemann Sums

Partial Fraction problem solution deviates from the Rule

Integration by parts: $\int(x+1)^2\ln(3x)\,dx$

How to integrate $\int\frac{\sin(kx)}{e^x}dx?$

Intuitive understanding of integrating a cumulative distribution function

Show that $\int_0^1\frac{\ln(x)^n}{x-1}dx=(-1)^{n+1}n!\zeta(n+1)$, for $n\geq 1$

Compute $\int\frac{x^2}{\tan{x}-x}dx$ for $x \in (0, \frac{\pi}{2})$

Necessary condition for improper integral of odd and even functions to converge

Find an appropriate trigonometric substitution of the form x=f(t) to simplify the integral

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