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Popular >

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

Solution

\int_{- 1}^{1} ∣ x ∣ - x^{2} d x

Solution

\frac{1}{3}

+1

Decimal

0.33333 \dots

Solution steps

\int_{- 1}^{1} ∣ x ∣ - x^{2} d x

Eliminate Absolutes

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

\int_{- 1}^{0} - x - x^{2} d x = \frac{1}{6}

\int_{0}^{1} x - x^{2} d x = \frac{1}{6}

= \frac{1}{6} + \frac{1}{6}

Simplify

\frac{1}{6} + \frac{1}{6} : \frac{1}{3}

= \frac{1}{3}

Graph

Popular Examples

integral from 0 to 1 of xsqrt(7x^2+9)

\int_{0}^{1} x 7 x^{2} + 9 d x

integral from 0 to 4 of 1/(4t^2+9)

\int_{0}^{4} \frac{1}{4 t ^{2} + 9} d t

integral from 0 to 1 of sqrt(x)(x^2-1)

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

integral from 0 to 1 of sin^2(npix)

\int_{0}^{1} sin^{2} (nπ x) d x

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

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

Frequently Asked Questions (FAQ)

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