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 Notation

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

\int_{0}^{\frac{π}{3}} 2 cos (x) + 3 d x

\int_{- 1}^{3} (2 x^{2} - x + 3)^{2} d x

\int_{0}^{1} (x^{2} + 3 x - 1) e^{x} d x

\int_{1}^{2} x^{2} e^{- x} d x

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