What is the integral from-6 to 6 of |x^2-25| ?

The integral from-6 to 6 of |x^2-25| is 532/3

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integral from-6 to 6 of |x^2-25|

\int_{- 6}^{6} x^{2} - 25 d x

\frac{532}{3}

Decimal

177.33333 \dots

Solution steps

\int_{- 6}^{6} x^{2} - 25 d x

Eliminate Absolutes

= \int_{- 6}^{- 5} x^{2} - 25 d x + \int_{- 5}^{5} - x^{2} + 25 d x + \int_{5}^{6} x^{2} - 25 d x

\int_{- 6}^{- 5} x^{2} - 25 d x = \frac{16}{3}

\int_{- 5}^{5} - x^{2} + 25 d x = \frac{500}{3}

\int_{5}^{6} x^{2} - 25 d x = \frac{16}{3}

= \frac{16}{3} + \frac{500}{3} + \frac{16}{3}

Simplify

\frac{16}{3} + \frac{500}{3} + \frac{16}{3} : \frac{532}{3}

= \frac{532}{3}

\int_{0}^{1} \frac{x}{x ^{2} + 3} d x

\int_{1}^{7} x^{2} - 2 x - 15 d x

\int_{0}^{7} x^{2} d x

\int_{- 5}^{3} ∣ x - 1 ∣ d x

\int_{0}^{2} x^{2} - 5 x + 6 d x

What is the integral from-6 to 6 of |x^2-25| ?
The integral from-6 to 6 of |x^2-25| is 532/3