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Popular >

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

Solution

\int_{0}^{3} ∣ 3 t - 8 ∣ d t

Solution

\frac{65}{6}

+1

Decimal

10.83333 \dots

Solution steps

\int_{0}^{3} ∣ 3 t - 8 ∣ d t

Eliminate Absolutes

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

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

\int_{\frac{8}{3}}^{3} 3 t - 8 d t = \frac{1}{6}

= \frac{32}{3} + \frac{1}{6}

Simplify

\frac{32}{3} + \frac{1}{6} : \frac{65}{6}

= \frac{65}{6}

Graph

Popular Examples

integral from 1 to 5 of (2x)/((x^2+1)^2)

\int_{1}^{5} \frac{2 x}{( x ^{2} + 1 ) ^{2}} d x

integral from 0 to 6 of 7/(8x^2+9x+1)

\int_{0}^{6} \frac{7}{8 x ^{2} + 9 x + 1} d x

integral from-1 to 1 of x/(1+|x|)

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

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

\int_{1}^{3} (3 x^{2} + 1) d x

integral from 1 to e of (2x^2+1)/x

\int_{1}^{e} \frac{2 x ^{2} + 1}{x} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of |3t-8| ?
The integral from 0 to 3 of |3t-8| is 65/6