What is the integral from-pi to pi of x^3cos(nx) ?

The integral from-pi to pi of x^3cos(nx) is 0

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integral from-pi to pi of x^3cos(nx)

\int_{- π}^{π} x^{3} cos (n x) d x

0

Solution steps

\int_{- π}^{π} x^{3} cos (n x) d x

If f(x) is an odd function and continuous at:

[- a, a]

then

\int_{- a}^{a} f (x) d x = 0

Parity of

x^{3} cos (n x) :

Odd

= 0

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What is the integral from-pi to pi of x^3cos(nx) ?
The integral from-pi to pi of x^3cos(nx) is 0