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Popular Calculus >

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

Solution

\int_{- 2}^{2} ∣ x - 1 ∣ d x

Solution

5

Solution steps

\int_{- 2}^{2} ∣ x - 1 ∣ d x

Eliminate Absolutes

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

\int_{- 2}^{1} - x + 1 d x = \frac{9}{2}

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

= \frac{9}{2} + \frac{1}{2}

Simplify

\frac{9}{2} + \frac{1}{2} : 5

= 5

Graph

Popular Examples

integral from 1 to 8 of 1/x

\int_{1}^{8} \frac{1}{x} d x

integral from 0 to 2 of sin((npix)/2)

\int_{0}^{2} sin (\frac{nπ x}{2}) d x

integral from-pi/2 to pi/2 of xcos(2x)

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

integral from 2 to 10 of 3/(sqrt(5x-1))

\int_{2}^{10} \frac{3}{5 x - 1} d x

integral from 2 to 4 of 1/(sqrt(x^2-4))

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

Frequently Asked Questions (FAQ)

What is the integral from-2 to 2 of |x-1| ?
The integral from-2 to 2 of |x-1| is 5