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Popular Calculus >

integral from 0 to 3 of |x^2-1|

Solution

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

Solution

\frac{22}{3}

+1

Decimal

7.33333 \dots

Solution steps

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

Eliminate Absolutes

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

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

\int_{1}^{3} x^{2} - 1 d x = \frac{20}{3}

= \frac{2}{3} + \frac{20}{3}

Simplify

\frac{2}{3} + \frac{20}{3} : \frac{22}{3}

= \frac{22}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of |x^2-1| ?
The integral from 0 to 3 of |x^2-1| is 22/3