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Popular >

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

Solution

\int_{0}^{5} ∣ 3 t - 8 ∣ d t

Solution

\frac{113}{6}

+1

Decimal

18.83333 \dots

Solution steps

\int_{0}^{5} ∣ 3 t - 8 ∣ d t

Eliminate Absolutes

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

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

\int_{\frac{8}{3}}^{5} 3 t - 8 d t = \frac{49}{6}

= \frac{32}{3} + \frac{49}{6}

Simplify

\frac{32}{3} + \frac{49}{6} : \frac{113}{6}

= \frac{113}{6}

Graph

Popular Examples

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

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

integral from 1 to 5 of-1/5 x+1

\int_{1}^{5} - \frac{1}{5} x + 1 d x

integral from 0 to 3 of 1/(sqrt(16+x^2))

\int_{0}^{3} \frac{1}{16 + x ^{2}} d x

integral from-2 to 2 of t^2

\int_{- 2}^{2} t^{2} d t

integral from-1 to 1 of (x+x^3)

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

Frequently Asked Questions (FAQ)

What is the integral from 0 to 5 of |3t-8| ?
The integral from 0 to 5 of |3t-8| is 113/6