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Popular >

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

Solution

\int_{- 2}^{2} ∣ x ∣ - ∣ x - 1 ∣ d x

Solution

- 1

Solution steps

\int_{- 2}^{2} ∣ x ∣ - ∣ x - 1 ∣ d x

Eliminate Absolutes

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

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

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

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

= - 2 + 0 + 1

Simplify

= - 1

Graph

Popular Examples

integral from 0 to 2 of (ti-t^3j+3t^5k)

\int_{0}^{2} (t i - t^{3} j + 3 t^{5} k) d t

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

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

integral from 0 to 3 of 2pi(10-x)(2x)

\int_{0}^{3} 2 π (10 - x) (2 x) d x

integral from 0 to 2pi of (1-cos(2θ))/2

\int_{0}^{2 π} \frac{1 - cos ( 2 θ )}{2} d θ

integral from 0 to x of 0.5x

\int_{0}^{x} 0.5 x d x

Frequently Asked Questions (FAQ)

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