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Popular Calculus >

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

Solution

\int_{0}^{2} ∣ 2 x - 1 ∣ d x

Solution

\frac{5}{2}

+1

Decimal

2.5

Solution steps

\int_{0}^{2} ∣ 2 x - 1 ∣ d x

Eliminate Absolutes

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

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

\int_{\frac{1}{2}}^{2} 2 x - 1 d x = \frac{9}{4}

= \frac{1}{4} + \frac{9}{4}

Simplify

\frac{1}{4} + \frac{9}{4} : \frac{5}{2}

= \frac{5}{2}

Graph

Popular Examples

taylor e^{x^2-x}

t a y l or e^{x^{2} - x}

integral of x/1

\int \frac{x}{1} d x

derivative of log_{10}(x^3+1)

d er i v a t i v e lo g_{10} (x^{3} + 1)

tangent of x^2+y^2=25,(3,4)

t an g e n t x^{2} + y^{2} = 25, (3, 4)

(\partial)/(\partial x)(-9x^2-7y^2)

\frac{\partial}{\partial x} (- 9 x^{2} - 7 y^{2})

Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of |2x-1| ?
The integral from 0 to 2 of |2x-1| is 5/2