What is the integral from-pi/3 to pi/3 of x^4sin(x) ?

The integral from-pi/3 to pi/3 of x^4sin(x) is 0

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integral from-pi/3 to pi/3 of x^4sin(x)

\int_{- \frac{π}{3}}^{\frac{π}{3}} x^{4} sin (x) d x

0

Solution steps

\int_{- \frac{π}{3}}^{\frac{π}{3}} x^{4} 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^{4} sin (x) :

Odd

= 0

\int_{0}^{a} (a^{2} x - x^{3}) d x

\int_{0}^{2} x^{3} - 4 x d x

\int_{- 3}^{6} ∣ x ∣ d x

\int_{1}^{4} \frac{1}{x + x} d x

\int_{1}^{e} \frac{ln ^{2} ( x )}{x} d x

What is the integral from-pi/3 to pi/3 of x^4sin(x) ?
The integral from-pi/3 to pi/3 of x^4sin(x) is 0