What is the integral from-4 to 4 of 5+sqrt(16-x^2) ?

The integral from-4 to 4 of 5+sqrt(16-x^2) is 40+8pi

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integral from-4 to 4 of 5+sqrt(16-x^2)

\int_{- 4}^{4} 5 + 16 - x^{2} d x

40 + 8 π

Decimal

65.13274 \dots

Solution steps

\int_{- 4}^{4} 5 + 16 - 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_{- 4}^{4} 5 d x + \int_{- 4}^{4} 16 - x^{2} d x

\int_{- 4}^{4} 5 d x = 40

\int_{- 4}^{4} 16 - x^{2} d x = 8 π

= 40 + 8 π

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

What is the integral from-4 to 4 of 5+sqrt(16-x^2) ?
The integral from-4 to 4 of 5+sqrt(16-x^2) is 40+8pi