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Popular >

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

Solution

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

Solution

\frac{44}{3}

+1

Decimal Notation

14.66666 \dots

Solution steps

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

Eliminate Absolutes

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

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

\int_{- 1}^{1} - x^{2} + 1 d x = \frac{4}{3}

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

= \frac{20}{3} + \frac{4}{3} + \frac{20}{3}

Simplify

\frac{20}{3} + \frac{4}{3} + \frac{20}{3} : \frac{44}{3}

= \frac{44}{3}

Popular Examples

integral from 0 to 1 of sqrt(81x^2+729)

\int_{0}^{1} 81 x^{2} + 729 d x

integral from 0 to 1/2 of 2arcsin(2y)

\int_{0}^{\frac{1}{2}} 2 arcsin (2 y) d y

integral from-3 to 2 of 1/((x+1)^3)

\int_{- 3}^{2} \frac{1}{( x + 1 ) ^{3}} d x

integral from 6 to 2 of x^3

\int_{6}^{2} x^{3} d x

integral from-pi to 0 of pisin(nx)

\int_{- π}^{0} π sin (n x) d x

Frequently Asked Questions (FAQ)

What is the integral from-3 to 3 of |x^2-1| ?
The integral from-3 to 3 of |x^2-1| is 44/3