What is the integral from-pi to pi of (x^2+sin^3(x)) ?

The integral from-pi to pi of (x^2+sin^3(x)) is (2pi^3)/3

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integral from-pi to pi of (x^2+sin^3(x))

\int_{- π}^{π} (x^{2} + sin^{3} (x)) d x

\frac{2 π ^{3}}{3}

Decimal

20.67085 \dots

Solution steps

\int_{- π}^{π} x^{2} + sin^{3} (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- π}^{π} x^{2} d x + \int_{- π}^{π} sin^{3} (x) d x

\int_{- π}^{π} x^{2} d x = \frac{2 π ^{3}}{3}

\int_{- π}^{π} sin^{3} (x) d x = 0

= \frac{2 π ^{3}}{3} + 0

Simplify

= \frac{2 π ^{3}}{3}

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What is the integral from-pi to pi of (x^2+sin^3(x)) ?
The integral from-pi to pi of (x^2+sin^3(x)) is (2pi^3)/3