What is the integral from-5 to 0 of (1+sqrt(25-x^2)) ?

The integral from-5 to 0 of (1+sqrt(25-x^2)) is 5+(25pi)/4

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integral from-5 to 0 of (1+sqrt(25-x^2))

\int_{- 5}^{0} (1 + 25 - x^{2}) d x

5 + \frac{25 π}{4}

Decimal

24.63495 \dots

Solution steps

\int_{- 5}^{0} 1 + 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}^{0} 1 d x + \int_{- 5}^{0} 25 - x^{2} d x

\int_{- 5}^{0} 1 d x = 5

\int_{- 5}^{0} 25 - x^{2} d x = \frac{25 π}{4}

= 5 + \frac{25 π}{4}

What is the integral from-5 to 0 of (1+sqrt(25-x^2)) ?
The integral from-5 to 0 of (1+sqrt(25-x^2)) is 5+(25pi)/4