What is the integral from-1 to 1 of x^2sin(npix) ?

The integral from-1 to 1 of x^2sin(npix) is 0

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integral from-1 to 1 of x^2sin(npix)

\int_{- 1}^{1} x^{2} sin (nπ x) d x

0

Solution steps

\int_{- 1}^{1} x^{2} sin (nπ 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 (nπ x) :

Odd

= 0

\int_{0}^{\frac{π}{2}} cos (2 t) d t

\int_{- π}^{0} - 2 cos^{2} (x) sin (x) d x

\int_{0}^{10} 25 - (t - 5)^{2} d t

\int_{2}^{5} (x^{3} - x^{2} + 8) d x

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

What is the integral from-1 to 1 of x^2sin(npix) ?
The integral from-1 to 1 of x^2sin(npix) is 0