What is the integral from-pi to pi of x^6sin(x) ?

The integral from-pi to pi of x^6sin(x) is 0

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integral from-pi to pi of x^6sin(x)

\int_{- π}^{π} x^{6} sin (x) d x

0

Solution steps

\int_{- π}^{π} x^{6} sin (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^{6} sin (x) :

Odd

= 0

\int_{0}^{1} x sin (x^{3}) d x

\int_{- 1}^{1} cos (\frac{π x}{2}) d x

\int_{0}^{1} (x^{2} - 2 x) d x

\int_{- 2}^{4} t^{3} - 9 t d t

\int_{0}^{3} 15 e^{3 x} d x

What is the integral from-pi to pi of x^6sin(x) ?
The integral from-pi to pi of x^6sin(x) is 0