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Popular Calculus >

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

Solution

\int_{0}^{3} ∣ 2 x - 3 ∣ d x

Solution

\frac{9}{2}

+1

Decimal

4.5

Solution steps

\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

y^{''}-y^'-6y=0,y(0)=2,y^'(0)=2

y^{^{''}} - y^{^{'}} - 6 y = 0, y (0) = 2, y^{^{'}} (0) = 2

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

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\int sin (\frac{nπ x}{l}) d x

integral from 0 to 3y-5 of xy^2

\int_{0}^{3 y - 5} x y^{2} d x

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\int e^{- y^{2}} d y

Frequently Asked Questions (FAQ)

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