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Popular >

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

Solution

\int_{0}^{3} ∣ 3 x - 8 ∣ d x

Solution

\frac{65}{6}

+1

Solution steps

\int_{0}^{3} ∣ 3 x - 8 ∣ d x

Eliminate Absolutes

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

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

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

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

Simplify

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

= \frac{65}{6}

Popular Examples

integral from 2x to x^2 of cos(t)sin(t)

\int_{2 x}^{x^{2}} cos (t) sin (t) d t

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

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

integral from 0 to 2 of x^2+x+1

\int_{0}^{2} x^{2} + x + 1 d x

integral from 2 to 3 of 1/(xln(x))

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

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

\int_{0}^{1} 3 x (x^{2} + 1)^{3} d x

Frequently Asked Questions (FAQ)

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