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Popular >

integral from 0 to 3 of |5t-8|

Solution

\int_{0}^{3} ∣ 5 t - 8 ∣ d t

Solution

\frac{113}{10}

+1

Solution steps

\int_{0}^{3} ∣ 5 t - 8 ∣ d t

Eliminate Absolutes

= \int_{0}^{\frac{8}{5}} - 5 t + 8 d t + \int_{\frac{8}{5}}^{3} 5 t - 8 d t

\int_{0}^{\frac{8}{5}} - 5 t + 8 d t = \frac{32}{5}

\int_{\frac{8}{5}}^{3} 5 t - 8 d t = \frac{49}{10}

= \frac{32}{5} + \frac{49}{10}

Simplify

\frac{32}{5} + \frac{49}{10} : \frac{113}{10}

= \frac{113}{10}

Popular Examples

integral from 0 to pi/2 of pi(cos(x))^2

\int_{0}^{\frac{π}{2}} π (cos (x))^{2} d x

integral from 1 to 4 of 4sqrt(x)

\int_{1}^{4} 4 x d x

integral from 0 to 2 of sqrt((x-1)^2)

\int_{0}^{2} (x - 1)^{2} d x

integral from 0 to 2x of ln(1+t)

\int_{0}^{2 x} ln (1 + t) d t

integral from 3 to 5 of ln(x)

\int_{3}^{5} ln (x) d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of |5t-8| ?
The integral from 0 to 3 of |5t-8| is 113/10