What is the integral from-2 to 2 of 1+sqrt(4-x^2) ?

The integral from-2 to 2 of 1+sqrt(4-x^2) is 4+2pi

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integral from-2 to 2 of 1+sqrt(4-x^2)

\int_{- 2}^{2} 1 + 4 - x^{2} d x

4 + 2 π

Decimal

10.28318 \dots

Solution steps

\int_{- 2}^{2} 1 + 4 - x^{2} 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} 1 d x + \int_{- 2}^{2} 4 - x^{2} d x

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

\int_{- 2}^{2} 4 - x^{2} d x = 2 π

= 4 + 2 π

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What is the integral from-2 to 2 of 1+sqrt(4-x^2) ?
The integral from-2 to 2 of 1+sqrt(4-x^2) is 4+2pi