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

The integral from-2 to 2 of (2+sqrt(4-x^2)) is 8+2pi

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

\int_{- 2}^{2} (2 + 4 - x^{2}) d x

8 + 2 π

Decimal

14.28318 \dots

Solution steps

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

\int_{- 2}^{2} 2 d x = 8

\int_{- 2}^{2} 4 - x^{2} d x = 2 π

= 8 + 2 π

\int_{- 1}^{8} 3 x + 1 d x

\int_{0}^{9} (x) d x

\int_{0}^{3} 4^{4 x} d x

\int_{1}^{8} 3 x d x

\int_{\frac{π}{3}}^{π} (sin (x)) d x

What is the integral from-2 to 2 of (2+sqrt(4-x^2)) ?
The integral from-2 to 2 of (2+sqrt(4-x^2)) is 8+2pi