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Popular >

integral from 0 to 4 of |5-3x|

Solution

\int_{0}^{4} ∣ 5 - 3 x ∣ d x

Solution

\frac{37}{3}

+1

Solution steps

\int_{0}^{4} ∣ 5 - 3 x ∣ d x

Eliminate Absolutes

= \int_{0}^{\frac{5}{3}} 5 - 3 x d x + \int_{\frac{5}{3}}^{4} - 5 + 3 x d x

\int_{0}^{\frac{5}{3}} 5 - 3 x d x = \frac{25}{6}

\int_{\frac{5}{3}}^{4} - 5 + 3 x d x = \frac{49}{6}

= \frac{25}{6} + \frac{49}{6}

Simplify

\frac{25}{6} + \frac{49}{6} : \frac{37}{3}

= \frac{37}{3}

Popular Examples

integral from 0 to 4 of (2x-1)^2

\int_{0}^{4} (2 x - 1)^{2} d x

integral from 0 to 4 of 2tsqrt(1+t^2)

\int_{0}^{4} 2 t 1 + t^{2} d t

integral from 0 to pi/2 of e^{-8x}cos(x)

\int_{0}^{\frac{π}{2}} e^{- 8 x} cos (x) d x

integral from 3 to 6 of x^2+3

\int_{3}^{6} x^{2} + 3 d x

integral from 1 to 6 of x/(sqrt(x+3))

\int_{1}^{6} \frac{x}{x + 3} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 4 of |5-3x| ?
The integral from 0 to 4 of |5-3x| is 37/3