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Popular >

integral from 0 to 2 of |3x-2|

Solution

\int_{0}^{2} ∣ 3 x - 2 ∣ d x

Solution

\frac{10}{3}

+1

Decimal Notation

3.33333 \dots

Solution steps

\int_{0}^{2} ∣ 3 x - 2 ∣ d x

Eliminate Absolutes

= \int_{0}^{\frac{2}{3}} - 3 x + 2 d x + \int_{\frac{2}{3}}^{2} 3 x - 2 d x

\int_{0}^{\frac{2}{3}} - 3 x + 2 d x = \frac{2}{3}

\int_{\frac{2}{3}}^{2} 3 x - 2 d x = \frac{8}{3}

= \frac{2}{3} + \frac{8}{3}

Simplify

\frac{2}{3} + \frac{8}{3} : \frac{10}{3}

= \frac{10}{3}

Popular Examples

integral from-1 to 0 of 3x^2e^{-x^3+1}

\int_{- 1}^{0} 3 x^{2} e^{- x^{3} + 1} d x

integral from 1 to infinity of 3/(e^x)

\int_{1}^{\infty} \frac{3}{e ^{x}} d x

integral from 0 to pi of 1/(2+cos(x))

\int_{0}^{π} \frac{1}{2 + cos ( x )} d x

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

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

integral from 0 to x of e^{3t^2}

\int_{0}^{x} e^{3 t^{2}} d t

Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of |3x-2| ?
The integral from 0 to 2 of |3x-2| is 10/3