What is the integral from-1 to 5 of sqrt(5+4x-x^2)+4 ?

The integral from-1 to 5 of sqrt(5+4x-x^2)+4 is (9pi)/2+24

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integral from-1 to 5 of sqrt(5+4x-x^2)+4

\int_{- 1}^{5} 5 + 4 x - x^{2} + 4 d x

\frac{9 π}{2} + 24

Decimal

38.13716 \dots

Solution steps

\int_{- 1}^{5} 5 + 4 x - x^{2} + 4 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_{- 1}^{5} 5 + 4 x - x^{2} d x + \int_{- 1}^{5} 4 d x

\int_{- 1}^{5} 5 + 4 x - x^{2} d x = \frac{9 π}{2}

\int_{- 1}^{5} 4 d x = 24

= \frac{9 π}{2} + 24

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What is the integral from-1 to 5 of sqrt(5+4x-x^2)+4 ?
The integral from-1 to 5 of sqrt(5+4x-x^2)+4 is (9pi)/2+24