What is the integral from-3 to 3 of |-x^2+5| ?

The integral from-3 to 3 of |-x^2+5| is -(20sqrt(5))/3+20sqrt(5)-12

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integral from-3 to 3 of |-x^2+5|

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

- \frac{20 5}{3} + 205 - 12

Decimal

17.81423 \dots

Solution steps

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

Eliminate Absolutes

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

\int_{- 3}^{- 5} x^{2} - 5 d x = - \frac{5 5}{3} + 55 - 6

\int_{- 5}^{5} - x^{2} + 5 d x = - \frac{10 5}{3} + 105

\int_{5}^{3} x^{2} - 5 d x = - \frac{5 5}{3} + 55 - 6

= - \frac{5 5}{3} + 55 - 6 - \frac{10 5}{3} + 105 - \frac{5 5}{3} + 55 - 6

Simplify

- \frac{5 5}{3} + 55 - 6 - \frac{10 5}{3} + 105 - \frac{5 5}{3} + 55 - 6 : - \frac{20 5}{3} + 205 - 12

= - \frac{20 5}{3} + 205 - 12

What is the integral from-3 to 3 of |-x^2+5| ?
The integral from-3 to 3 of |-x^2+5| is -(20sqrt(5))/3+20sqrt(5)-12