What is the integral from-6 to 0 of 5+sqrt(36-x^2) ?

The integral from-6 to 0 of 5+sqrt(36-x^2) is 30+9pi

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integral from-6 to 0 of 5+sqrt(36-x^2)

\int_{- 6}^{0} 5 + 36 - x^{2} d x

30 + 9 π

Decimal

58.27433 \dots

Solution steps

\int_{- 6}^{0} 5 + 36 - 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_{- 6}^{0} 5 d x + \int_{- 6}^{0} 36 - x^{2} d x

\int_{- 6}^{0} 5 d x = 30

\int_{- 6}^{0} 36 - x^{2} d x = 9 π

= 30 + 9 π

\int_{- 1}^{1} (3 x - 9) d x

\int_{- \infty}^{- 1} x^{- \frac{13}{5}} d x

\int_{0}^{π} (sin (2 x)) d x

\int_{0}^{1} (3 y)^{2} d y

\int_{- 1}^{3} 6 x y - 5 e^{y} d x

What is the integral from-6 to 0 of 5+sqrt(36-x^2) ?
The integral from-6 to 0 of 5+sqrt(36-x^2) is 30+9pi