What is the integral from-2pi to 2pi of x^2sin(2x) ?

The integral from-2pi to 2pi of x^2sin(2x) is 0

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integral from-2pi to 2pi of x^2sin(2x)

\int_{- 2 π}^{2 π} x^{2} sin (2 x) d x

0

Solution steps

\int_{- 2 π}^{2 π} x^{2} sin (2 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^{2} sin (2 x) :

Odd

= 0

\int_{- 2}^{2} - x^{2} d x

\int_{0}^{4} 2 x x^{2} + 9 d x

\int_{0}^{4} ∣ 2 - x ∣ d x

\int_{0}^{4} \frac{1}{4 - x} d x

\int_{0}^{π} sin (x) cos^{3} (x) d x

What is the integral from-2pi to 2pi of x^2sin(2x) ?
The integral from-2pi to 2pi of x^2sin(2x) is 0