What is the integral from-2 to 2 of (5-3sqrt(4-x^2)) ?

The integral from-2 to 2 of (5-3sqrt(4-x^2)) is 20-6pi

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integral from-2 to 2 of (5-3sqrt(4-x^2))

\int_{- 2}^{2} (5 - 3 4 - x^{2}) d x

20 - 6 π

Decimal

1.15044 \dots

Solution steps

\int_{- 2}^{2} 5 - 3 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} 5 d x - \int_{- 2}^{2} 3 4 - x^{2} d x

\int_{- 2}^{2} 5 d x = 20

\int_{- 2}^{2} 3 4 - x^{2} d x = 6 π

= 20 - 6 π

\int_{0}^{1} 6 6 x d x

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

\int_{0}^{π} e^{i t} d t

\int_{0}^{4} (x + 2) d x

What is the integral from-2 to 2 of (5-3sqrt(4-x^2)) ?
The integral from-2 to 2 of (5-3sqrt(4-x^2)) is 20-6pi