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Popular Calculus >

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

Solution

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

Solution

\frac{32}{3}

+1

Decimal

10.66666 \dots

Solution steps

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

Eliminate Absolutes

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{- 2}^{2} 4 d x = 16

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

= 16 - \frac{16}{3}

Simplify

16 - \frac{16}{3} : \frac{32}{3}

= \frac{32}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from-2 to 2 of |4-x^2| ?
The integral from-2 to 2 of |4-x^2| is 32/3