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Popular >

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

Solution

\int_{3}^{0} ∣ 2 x - 3 ∣ d x

Solution

- \frac{9}{2}

+1

Decimal

- 4.5

Solution steps

\int_{3}^{0} ∣ 2 x - 3 ∣ d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{3} ∣ 2 x - 3 ∣ d x

Eliminate Absolutes

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

\int_{0}^{\frac{3}{2}} - 2 x + 3 d x = \frac{9}{4}

\int_{\frac{3}{2}}^{3} 2 x - 3 d x = \frac{9}{4}

= - (\frac{9}{4} + \frac{9}{4})

Simplify

- (\frac{9}{4} + \frac{9}{4}) : - \frac{9}{2}

= - \frac{9}{2}

Graph

Popular Examples

integral from 1 to 3 of 6x^2

\int_{1}^{3} 6 x^{2} d x

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

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

integral from 0 to pi/6 of sin(x)

\int_{0}^{\frac{π}{6}} sin (x) d x

integral from 0 to x of t^2

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

integral from 0 to 2 of x/(sqrt(x^2+5))

\int_{0}^{2} \frac{x}{x ^{2} + 5} d x

Frequently Asked Questions (FAQ)

What is the integral from 3 to 0 of |2x-3| ?
The integral from 3 to 0 of |2x-3| is -9/2