What is the integral from-3 to 0 of x+3+sqrt(9-x^2) ?

The integral from-3 to 0 of x+3+sqrt(9-x^2) is 9/2+(9pi)/4

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integral from-3 to 0 of x+3+sqrt(9-x^2)

\int_{- 3}^{0} x + 3 + 9 - x^{2} d x

\frac{9}{2} + \frac{9 π}{4}

Solution steps

\int_{- 3}^{0} x + 3 + 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}^{0} x d x + \int_{- 3}^{0} 3 d x + \int_{- 3}^{0} 9 - x^{2} d x

\int_{- 3}^{0} x d x = - \frac{9}{2}

\int_{- 3}^{0} 3 d x = 9

\int_{- 3}^{0} 9 - x^{2} d x = \frac{9 π}{4}

= - \frac{9}{2} + 9 + \frac{9 π}{4}

Simplify

- \frac{9}{2} + 9 + \frac{9 π}{4} : \frac{9}{2} + \frac{9 π}{4}

= \frac{9}{2} + \frac{9 π}{4}

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

\int_{0}^{\frac{π}{2}} (cos (2 x)) d x

\int_{1}^{2} t 9 + 16 t^{2} d t

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

\int_{0}^{1} \frac{1}{x ^{3} + x ^{2} + 2 x + 2} d x

What is the integral from-3 to 0 of x+3+sqrt(9-x^2) ?
The integral from-3 to 0 of x+3+sqrt(9-x^2) is 9/2+(9pi)/4