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Popular Calculus >

integral from 0 to 4 of |3t-8|

Solution

\int_{0}^{4} ∣ 3 t - 8 ∣ d t

Solution

\frac{40}{3}

+1

Decimal

13.33333 \dots

Solution steps

\int_{0}^{4} ∣ 3 t - 8 ∣ d t

Eliminate Absolutes

= \int_{0}^{\frac{8}{3}} - 3 t + 8 d t + \int_{\frac{8}{3}}^{4} 3 t - 8 d t

\int_{0}^{\frac{8}{3}} - 3 t + 8 d t = \frac{32}{3}

\int_{\frac{8}{3}}^{4} 3 t - 8 d t = \frac{8}{3}

= \frac{32}{3} + \frac{8}{3}

Simplify

\frac{32}{3} + \frac{8}{3} : \frac{40}{3}

= \frac{40}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 4 of |3t-8| ?
The integral from 0 to 4 of |3t-8| is 40/3