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Popular Calculus >

integral from-3 to 4 of |x^2-4|

Solution

\int_{- 3}^{4} x^{2} - 4 d x

Solution

\frac{71}{3}

+1

Decimal

23.66666 \dots

Solution steps

\int_{- 3}^{4} x^{2} - 4 d x

Eliminate Absolutes

= \int_{- 3}^{- 2} x^{2} - 4 d x + \int_{- 2}^{2} - x^{2} + 4 d x + \int_{2}^{4} x^{2} - 4 d x

\int_{- 3}^{- 2} x^{2} - 4 d x = \frac{7}{3}

\int_{- 2}^{2} - x^{2} + 4 d x = \frac{32}{3}

\int_{2}^{4} x^{2} - 4 d x = \frac{32}{3}

= \frac{7}{3} + \frac{32}{3} + \frac{32}{3}

Simplify

\frac{7}{3} + \frac{32}{3} + \frac{32}{3} : \frac{71}{3}

= \frac{71}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from-3 to 4 of |x^2-4| ?
The integral from-3 to 4 of |x^2-4| is 71/3