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Popular >

integral from 0 to 3 of |2x-1|

Solution

\int_{0}^{3} ∣ 2 x - 1 ∣ d x

Solution

\frac{13}{2}

+1

Decimal Notation

6.5

Solution steps

\int_{0}^{3} ∣ 2 x - 1 ∣ d x

Eliminate Absolutes

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

\int_{0}^{\frac{1}{2}} - 2 x + 1 d x = \frac{1}{4}

\int_{\frac{1}{2}}^{3} 2 x - 1 d x = \frac{25}{4}

= \frac{1}{4} + \frac{25}{4}

Simplify

\frac{1}{4} + \frac{25}{4} : \frac{13}{2}

= \frac{13}{2}

Popular Examples

(x^2+1)(dy)/(dx)=xy

(x^{2} + 1) \frac{d y}{d x} = x y

integral of (x^2)/(1+2x^2)

\int \frac{x ^{2}}{1 + 2 x ^{2}} d x

integral from 2 to infinity of-5x^{-2}

\int_{2}^{\infty} - 5 x^{- 2} d x

derivative of 5xe^{4x}

\frac{d}{d x} (5 x e^{4 x})

(\partial)/(\partial x)((63)/((9+x^2+y^2)))

\frac{\partial}{\partial x} (\frac{63}{( 9 + x ^{2} + y ^{2} )})

Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of |2x-1| ?
The integral from 0 to 3 of |2x-1| is 13/2