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Popular >

integral from 0 to 8 of |x-3|

Solution

\int_{0}^{8} ∣ x - 3 ∣ d x

Solution

17

Solution steps

\int_{0}^{8} ∣ x - 3 ∣ d x

Eliminate Absolutes

= \int_{0}^{3} - x + 3 d x + \int_{3}^{8} x - 3 d x

\int_{0}^{3} - x + 3 d x = \frac{9}{2}

\int_{3}^{8} x - 3 d x = \frac{25}{2}

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

Simplify

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

= 17

Popular Examples

integral from 0 to 1 of 4x-6(x^2)^{1/3}

\int_{0}^{1} 4 x - 6 (x^{2})^{\frac{1}{3}} d x

integral from-1 to 3 of (3x-5)(x+2)

\int_{- 1}^{3} (3 x - 5) (x + 2) d x

integral from-3 to 2 of x^2-(6-x)

\int_{- 3}^{2} x^{2} - (6 - x) d x

integral from 2 to 4 of 8-2x

\int_{2}^{4} 8 - 2 x d x

integral from 0 to 3 of x^2-2x-3

\int_{0}^{3} x^{2} - 2 x - 3 d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 8 of |x-3| ?
The integral from 0 to 8 of |x-3| is 17