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Popular Calculus >

integral from 0 to 5 of |2x-5|

Solution

\int_{0}^{5} ∣ 2 x - 5 ∣ d x

Solution

\frac{25}{2}

+1

Decimal

12.5

Solution steps

\int_{0}^{5} ∣ 2 x - 5 ∣ d x

Eliminate Absolutes

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

\int_{0}^{\frac{5}{2}} - 2 x + 5 d x = \frac{25}{4}

\int_{\frac{5}{2}}^{5} 2 x - 5 d x = \frac{25}{4}

= \frac{25}{4} + \frac{25}{4}

Simplify

\frac{25}{4} + \frac{25}{4} : \frac{25}{2}

= \frac{25}{2}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 5 of |2x-5| ?
The integral from 0 to 5 of |2x-5| is 25/2