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Popular >

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

Solution

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

Solution

\frac{46}{3}

+1

Decimal Notation

15.33333 \dots

Solution steps

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

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

Simplify

\frac{7}{3} + \frac{32}{3} + \frac{7}{3} : \frac{46}{3}

= \frac{46}{3}

Popular Examples

integral from 0 to 1 of (2e^{x/3+4}+5)

\int_{0}^{1} (2 e^{\frac{x}{3} + 4} + 5) d x

integral from 0 to 4 of 2x^2

\int_{0}^{4} 2 x^{2} d x

integral from 1 to e^3 of (ln(x))/x

\int_{1}^{e^{3}} \frac{ln ( x )}{x} d x

integral from 0 to 1 of x^2(5x^3-1)^4

\int_{0}^{1} x^{2} (5 x^{3} - 1)^{4} d x

integral from-3 to 2 of (3x^2-5x)

\int_{- 3}^{2} (3 x^{2} - 5 x) d x

Frequently Asked Questions (FAQ)

What is the integral from-3 to 3 of |x^2-4| ?
The integral from-3 to 3 of |x^2-4| is 46/3