What is the integral from-7 to 7 of |x^2-36| ?

The integral from-7 to 7 of |x^2-36| is 902/3

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integral from-7 to 7 of |x^2-36|

\int_{- 7}^{7} x^{2} - 36 d x

\frac{902}{3}

Decimal

300.66666 \dots

Solution steps

\int_{- 7}^{7} x^{2} - 36 d x

Eliminate Absolutes

= \int_{- 7}^{- 6} x^{2} - 36 d x + \int_{- 6}^{6} - x^{2} + 36 d x + \int_{6}^{7} x^{2} - 36 d x

\int_{- 7}^{- 6} x^{2} - 36 d x = \frac{19}{3}

\int_{- 6}^{6} - x^{2} + 36 d x = 288

\int_{6}^{7} x^{2} - 36 d x = \frac{19}{3}

= \frac{19}{3} + 288 + \frac{19}{3}

Simplify

\frac{19}{3} + 288 + \frac{19}{3} : \frac{902}{3}

= \frac{902}{3}

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What is the integral from-7 to 7 of |x^2-36| ?
The integral from-7 to 7 of |x^2-36| is 902/3