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Popular >

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

Solution

\int_{- 1}^{1} 1 - ∣ x ∣ x d x

Solution

2

Solution steps

\int_{- 1}^{1} 1 - ∣ x ∣ x d x

Eliminate Absolutes

= \int_{- 1}^{0} 1 - (- x) x d x + \int_{0}^{1} 1 - xx d x

\int_{- 1}^{0} 1 - (- x) x d x = \frac{4}{3}

\int_{0}^{1} 1 - xx d x = \frac{2}{3}

= \frac{4}{3} + \frac{2}{3}

Simplify

\frac{4}{3} + \frac{2}{3} : 2

= 2

Popular Examples

integral from 0 to 2 of ((x-2)^2)/2

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

integral from 3 to 9 of 20e^{-0.1x^2}

\int_{3}^{9} 20 e^{- 0.1 x^{2}} d x

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

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

integral from 0 to 1 of (x^2)/(1+y^2)

\int_{0}^{1} \frac{x ^{2}}{1 + y ^{2}} d y

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

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

Frequently Asked Questions (FAQ)

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