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Popular >

integral from 0 to 8 of |x-5|

Solution

\int_{0}^{8} ∣ x - 5 ∣ d x

Solution

17

Solution steps

\int_{0}^{8} ∣ x - 5 ∣ d x

Eliminate Absolutes

= \int_{0}^{5} - x + 5 d x + \int_{5}^{8} x - 5 d x

\int_{0}^{5} - x + 5 d x = \frac{25}{2}

\int_{5}^{8} x - 5 d x = \frac{9}{2}

= \frac{25}{2} + \frac{9}{2}

Simplify

\frac{25}{2} + \frac{9}{2} : 17

= 17

Popular Examples

integral from-2 to-4 of (x+4)^{10}

\int_{- 2}^{- 4} (x + 4)^{10} d x

integral from-1 to 1 of (1-x^4)

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

integral from-1 to 1 of kx^2

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

integral from 0 to 1 of xsqrt(x^2+3)

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

integral from-1 to 1 of t^3

\int_{- 1}^{1} t^{3} d t

Frequently Asked Questions (FAQ)

What is the integral from 0 to 8 of |x-5| ?
The integral from 0 to 8 of |x-5| is 17