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Popular >

integral from 0 to 2 of |2-x|

Solution

\int_{0}^{2} ∣ 2 - x ∣ d x

Solution

2

Solution steps

\int_{0}^{2} ∣ 2 - x ∣ d x

Eliminate Absolutes

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{0}^{2} 2 d x = 4

\int_{0}^{2} x d x = 2

= 4 - 2

Simplify

= 2

Popular Examples

integral from 0 to pi of 1/(1+sin(x))

\int_{0}^{π} \frac{1}{1 + sin ( x )} d x

integral from-3 to 2 of (2x^3-4x)

\int_{- 3}^{2} (2 x^{3} - 4 x) d x

integral from 0 to 2 of sqrt(4x-x^2)

\int_{0}^{2} 4 x - x^{2} d x

integral from 1 to 5 of t^2-2t-8

\int_{1}^{5} t^{2} - 2 t - 8 d t

integral from-3 to 2 of 12-x^2-x

\int_{- 3}^{2} 12 - x^{2} - x d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of |2-x| ?
The integral from 0 to 2 of |2-x| is 2