What is the integral from-1 to 1 of x(x^3+cos^3(x)) ?

The integral from-1 to 1 of x(x^3+cos^3(x)) is 2/5

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integral from-1 to 1 of x(x^3+cos^3(x))

\int_{- 1}^{1} x (x^{3} + cos^{3} (x)) d x

\frac{2}{5}

Decimal

0.4

Solution steps

\int_{- 1}^{1} x (x^{3} + cos^{3} (x)) d x

Expand

x (x^{3} + cos^{3} (x)) : x^{4} + x cos^{3} (x)

= \int_{- 1}^{1} x^{4} + x cos^{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_{- 1}^{1} x^{4} d x + \int_{- 1}^{1} x cos^{3} (x) d x

\int_{- 1}^{1} x^{4} d x = \frac{2}{5}

\int_{- 1}^{1} x cos^{3} (x) d x = 0

= \frac{2}{5} + 0

Simplify

= \frac{2}{5}

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What is the integral from-1 to 1 of x(x^3+cos^3(x)) ?
The integral from-1 to 1 of x(x^3+cos^3(x)) is 2/5