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Popular >

integral from 1 to 3 of |x-2|

Solution

\int_{1}^{3} ∣ x - 2 ∣ d x

Solution

1

Solution steps

\int_{1}^{3} ∣ x - 2 ∣ d x

Eliminate Absolutes

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

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

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

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

Simplify

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

= 1

Popular Examples

integral from 1 to infinity of cos(x)

\int_{1}^{\infty} cos (x) d x

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

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

integral from 0 to 1 of x^3e^{2x}

\int_{0}^{1} x^{3} e^{2 x} d x

integral from 0 to 5 of 3

\int_{0}^{5} 3 d x

integral from 0 to 4 of cos(sqrt(x)-1)

\int_{0}^{4} cos (x - 1) d x

Frequently Asked Questions (FAQ)

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