What is the integral from-2 to 2 of sqrt(4-x^2)+x^3 ?

The integral from-2 to 2 of sqrt(4-x^2)+x^3 is 2pi

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integral from-2 to 2 of sqrt(4-x^2)+x^3

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

2 π

Decimal

6.28318 \dots

Solution steps

\int_{- 2}^{2} 4 - x^{2} + x^{3} 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_{- 2}^{2} 4 - x^{2} d x + \int_{- 2}^{2} x^{3} d x

\int_{- 2}^{2} 4 - x^{2} d x = 2 π

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

= 2 π + 0

Simplify

= 2 π

What is the integral from-2 to 2 of sqrt(4-x^2)+x^3 ?
The integral from-2 to 2 of sqrt(4-x^2)+x^3 is 2pi