What is the integral from 2 to 6 of |-x^2+8| ?

The integral from 2 to 6 of |-x^2+8| is 32sqrt(2)+(-32sqrt(2)+8)/3+8

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integral from 2 to 6 of |-x^2+8|

\int_{2}^{6} - x^{2} + 8 d x

322 + \frac{- 32 2 + 8}{3} + 8

Solution steps

\int_{2}^{6} - x^{2} + 8 d x

Eliminate Absolutes

= \int_{2}^{22} - x^{2} + 8 d x + \int_{22}^{6} x^{2} - 8 d x

\int_{2}^{22} - x^{2} + 8 d x = - \frac{16 2 - 8}{3} + 162 - 16

\int_{22}^{6} x^{2} - 8 d x = - \frac{16 2}{3} + 24 + 162

= - \frac{16 2 - 8}{3} + 162 - 16 - \frac{16 2}{3} + 24 + 162

Simplify

- \frac{16 2 - 8}{3} + 162 - 16 - \frac{16 2}{3} + 24 + 162 : 322 + \frac{- 32 2 + 8}{3} + 8

= 322 + \frac{- 32 2 + 8}{3} + 8

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What is the integral from 2 to 6 of |-x^2+8| ?
The integral from 2 to 6 of |-x^2+8| is 32sqrt(2)+(-32sqrt(2)+8)/3+8