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Popular >

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

Solution

\int_{0}^{5} ∣ 2 t - 5 ∣ d t

Solution

\frac{25}{2}

+1

Solution steps

\int_{0}^{5} ∣ 2 t - 5 ∣ d t

Eliminate Absolutes

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

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

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

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

Simplify

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

= \frac{25}{2}

Popular Examples

integral from 0 to 3 of sin^2(x)

\int_{0}^{3} sin^{2} (x) d x

integral from 0 to x of 1/(x-1)

\int_{0}^{x} \frac{1}{x - 1} d x

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

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

integral from 0 to infinity of xe^{-kx}

\int_{0}^{\infty} x e^{- k x} d x

integral from 1 to 3 of sqrt(x^2+8)

\int_{1}^{3} x^{2} + 8 d x

Frequently Asked Questions (FAQ)

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