What is the integral from 0 to 8 of |8-x^2| ?

The integral from 0 to 8 of |8-x^2| is 32sqrt(2)+(-32sqrt(2)+512)/3-64

Popular >

integral from 0 to 8 of |8-x^2|

\int_{0}^{8} 8 - x^{2} d x

322 + \frac{- 32 2 + 512}{3} - 64

Decimal Notation

136.83655 \dots

Solution steps

\int_{0}^{8} 8 - x^{2} d x

Eliminate Absolutes

= \int_{0}^{22} 8 - x^{2} d x + \int_{22}^{8} - 8 + x^{2} d x

\int_{0}^{22} 8 - x^{2} d x = 162 - \frac{16 2}{3}

\int_{22}^{8} - 8 + x^{2} d x = - 64 + 162 + \frac{512 - 16 2}{3}

= 162 - \frac{16 2}{3} - 64 + 162 + \frac{512 - 16 2}{3}

Simplify

162 - \frac{16 2}{3} - 64 + 162 + \frac{512 - 16 2}{3} : 322 + \frac{- 32 2 + 512}{3} - 64

= 322 + \frac{- 32 2 + 512}{3} - 64

\int_{0}^{1} 6 x (x - x^{2}) d x

\int_{0}^{1} 2 x (3 x - 2)^{6} d x

\int_{1}^{e} x ln (x^{2}) d x

\int_{- 1}^{1} \frac{x}{x ^{2} + 2} d x

\int_{1}^{3} 1 - (y - 2)^{2} d y

What is the integral from 0 to 8 of |8-x^2| ?
The integral from 0 to 8 of |8-x^2| is 32sqrt(2)+(-32sqrt(2)+512)/3-64