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Calculate $\lim_{n\rightarrow \infty}n\ \int_0^n \sin^2(\pi x)\left(\frac{1}{(x-1)(x-2)}+\frac{1}{(x+1)(x+2)}\right) dx$

calculus integration limits

answered 2 mins ago Jack D'Aurizio 74.8k

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Sum of waves with random phase and amplitudes as random sum of cosines

probability statistics

asked 7 mins ago user1260450 1

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Calculate the integral : $\iiint_G xysin(yz)$ While $0\leq x\leq\pi, 0 \leq y \leq 1, 0\leq z \leq \pi/6$

calculus integration definite-integrals

modified 17 secs ago danimal 1,406

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If $x ^ 6 = x$, prove that $x ^ 2 = x$, in a ring

abstract-algebra ring-theory

modified 14 mins ago Mathmo123 9,569

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Making Change for a Dollar (and other number partitioning problems)

combinatorics generating-functions partitions

modified 14 mins ago Marc van Leeuwen 60.1k

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Calculating determinant of a Vandermonde type matrix of order n

linear-algebra

answered 15 secs ago egreg 51.1k

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combination problem

combinatorics

modified 17 mins ago ashiwn 6

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Direction on how to rightly compute a certain expected value.

probability random-variables

modified 18 mins ago drhab 28.7k

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Help with $\int_{0}^{T} I_{0}(2\sqrt{ y x})\cos(tx)dx$

integration analysis

asked 28 mins ago Mohammad Al Jamal 58

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An identity with determinant and trace of a matrix

linear-algebra determinant trace symmetric-polynomials

asked 30 mins ago Jason 154

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Is every open cover of a smooth manifold finer than a cover built from the union of disjoint open sets?

general-topology differential-geometry geometric-topology

modified 32 mins ago John 10.6k

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Find the first few coefficients in the function represented as a power series

calculus

modified 33 mins ago Community♦ 1

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Calculating this integral

calculus integration

modified 33 mins ago Yves Daoust 19.6k

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Finding a weight function with a specific property

calculus examples-counterexamples

asked 33 mins ago user159517 638

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Calculate $\lim_{n\rightarrow \infty}n\ \int_0^n \sin^2(\pi x)\left(\frac{1}{(x-1)(x-2)}+\frac{1}{(x+1)(x+2)}\right) dx$

Sum of waves with random phase and amplitudes as random sum of cosines

Calculate the integral : $\iiint_G xysin(yz)$ While $0\leq x\leq\pi, 0 \leq y \leq 1, 0\leq z \leq \pi/6$

If $x ^ 6 = x$, prove that $x ^ 2 = x$, in a ring

Making Change for a Dollar (and other number partitioning problems)

Calculating determinant of a Vandermonde type matrix of order n

combination problem

Direction on how to rightly compute a certain expected value.

Help with $\int_{0}^{T} I_{0}(2\sqrt{ y x})\cos(tx)dx$

An identity with determinant and trace of a matrix

Is every open cover of a smooth manifold finer than a cover built from the union of disjoint open sets?

Find the first few coefficients in the function represented as a power series

Calculating this integral

Finding a weight function with a specific property

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