What is the integral from-9 to 0 of (1+sqrt(81-x^2)) ?

The integral from-9 to 0 of (1+sqrt(81-x^2)) is 9+(81pi)/4

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integral from-9 to 0 of (1+sqrt(81-x^2))

\int_{- 9}^{0} (1 + 81 - x^{2}) d x

9 + \frac{81 π}{4}

Decimal

72.61725 \dots

Solution steps

\int_{- 9}^{0} 1 + 81 - 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_{- 9}^{0} 1 d x + \int_{- 9}^{0} 81 - x^{2} d x

\int_{- 9}^{0} 1 d x = 9

\int_{- 9}^{0} 81 - x^{2} d x = \frac{81 π}{4}

= 9 + \frac{81 π}{4}

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What is the integral from-9 to 0 of (1+sqrt(81-x^2)) ?
The integral from-9 to 0 of (1+sqrt(81-x^2)) is 9+(81pi)/4