What is the integral from-3 to 3 of (5+sqrt(9-x^2)) ?

The integral from-3 to 3 of (5+sqrt(9-x^2)) is 30+(9pi)/2

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integral from-3 to 3 of (5+sqrt(9-x^2))

\int_{- 3}^{3} (5 + 9 - x^{2}) d x

30 + \frac{9 π}{2}

Solution steps

\int_{- 3}^{3} 5 + 9 - 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_{- 3}^{3} 5 d x + \int_{- 3}^{3} 9 - x^{2} d x

\int_{- 3}^{3} 5 d x = 30

\int_{- 3}^{3} 9 - x^{2} d x = \frac{9 π}{2}

= 30 + \frac{9 π}{2}

\int_{0}^{1} e^{- x} (4 - e^{x}) d x

\int_{0}^{3} 0.3 e^{x} d x

\int_{0}^{2} e^{- r^{2}} r d r

\int_{0}^{2} r 4 - r^{2} d r

\int_{- 1}^{1} e^{- 2 x} d x

What is the integral from-3 to 3 of (5+sqrt(9-x^2)) ?
The integral from-3 to 3 of (5+sqrt(9-x^2)) is 30+(9pi)/2