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 Notation

1.71681 \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}^{0} (2 x + 1)^{3} d x

\int_{1}^{2} (\frac{1}{y} + \frac{2}{3}) d y

\int_{0}^{1} (arcsin (t))^{2} d t

\int_{1}^{3} x y^{2} + x^{2} + y + 4

\int_{0}^{4} \frac{4}{x ^{2} + 9} 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