What is the integral from 0 to pi of (x+sin^3(x)) ?

The integral from 0 to pi of (x+sin^3(x)) is (pi^2)/2+4/3

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integral from 0 to pi of (x+sin^3(x))

\int_{0}^{π} (x + sin^{3} (x)) d x

\frac{π ^{2}}{2} + \frac{4}{3}

Decimal Notation

6.26813 \dots

Solution steps

\int_{0}^{π} x + 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_{0}^{π} x d x + \int_{0}^{π} sin^{3} (x) d x

\int_{0}^{π} x d x = \frac{π ^{2}}{2}

\int_{0}^{π} sin^{3} (x) d x = \frac{4}{3}

= \frac{π ^{2}}{2} + \frac{4}{3}

\int_{0}^{2} x cos (\frac{nπ}{2} x) d x

\int_{0}^{1} \frac{1}{y + 1} d y

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

\int_{2}^{5} \frac{1}{x - 1} d x

\int_{0}^{1} \frac{4}{t ^{2} + 1} d t

What is the integral from 0 to pi of (x+sin^3(x)) ?
The integral from 0 to pi of (x+sin^3(x)) is (pi^2)/2+4/3