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Popular >

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

Solution

\int_{- 1}^{1} x ∣ 2 x - 1 ∣ d x

Solution

- \frac{11}{12}

+1

Decimal Notation

- 0.91666 \dots

Solution steps

\int_{- 1}^{1} x ∣ 2 x - 1 ∣ d x

Eliminate Absolutes

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

\int_{- 1}^{\frac{1}{2}} x (- 2 x + 1) d x = - \frac{9}{8}

\int_{\frac{1}{2}}^{1} x (2 x - 1) d x = \frac{5}{24}

= - \frac{9}{8} + \frac{5}{24}

Simplify

- \frac{9}{8} + \frac{5}{24} : - \frac{11}{12}

= - \frac{11}{12}

Popular Examples

integral from 0 to 1 of (x+1)e^{2x}

\int_{0}^{1} (x + 1) e^{2 x} d x

integral from 2 to 4 of x^3+4x^2

\int_{2}^{4} x^{3} + 4 x^{2} d x

integral from 0 to 1 of (x^4y+y^2)

\int_{0}^{1} (x^{4} y + y^{2}) d y

integral from 0 to 5 of 1/(x^{0.4)}

\int_{0}^{5} \frac{1}{x ^{0.4}} d x

integral from-0.25 to 0.25 of (cos(x))^2

\int_{- 0.25}^{0.25} (cos (x))^{2} d x

Frequently Asked Questions (FAQ)

What is the integral from-1 to 1 of x|2x-1| ?
The integral from-1 to 1 of x|2x-1| is -11/12