What is the integral from-5 to 5 of (5+sqrt(25-x^2)) ?

The integral from-5 to 5 of (5+sqrt(25-x^2)) is 50+(25pi)/2

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integral from-5 to 5 of (5+sqrt(25-x^2))

\int_{- 5}^{5} (5 + 25 - x^{2}) d x

50 + \frac{25 π}{2}

Decimal

89.26990 \dots

Solution steps

\int_{- 5}^{5} 5 + 25 - 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_{- 5}^{5} 5 d x + \int_{- 5}^{5} 25 - x^{2} d x

\int_{- 5}^{5} 5 d x = 50

\int_{- 5}^{5} 25 - x^{2} d x = \frac{25 π}{2}

= 50 + \frac{25 π}{2}

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What is the integral from-5 to 5 of (5+sqrt(25-x^2)) ?
The integral from-5 to 5 of (5+sqrt(25-x^2)) is 50+(25pi)/2