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Popular >

integral from 0 to 6 of |x^2-4x|

Solution

\int_{0}^{6} x^{2} - 4 x d x

Solution

\frac{64}{3}

+1

Decimal Notation

21.33333 \dots

Solution steps

\int_{0}^{6} x^{2} - 4 x d x

Eliminate Absolutes

= \int_{0}^{4} - x^{2} + 4 x d x + \int_{4}^{6} x^{2} - 4 x d x

\int_{0}^{4} - x^{2} + 4 x d x = \frac{32}{3}

\int_{4}^{6} x^{2} - 4 x d x = \frac{32}{3}

= \frac{32}{3} + \frac{32}{3}

Simplify

\frac{32}{3} + \frac{32}{3} : \frac{64}{3}

= \frac{64}{3}

Popular Examples

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

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

integral from 1 to 4 of 3sqrt(x-1)

\int_{1}^{4} 3 x - 1 d x

integral from 1 to 3 of 12sin(6x-5)

\int_{1}^{3} 12 sin (6 x - 5) d x

integral from 1 to infinity of 2/(x^5)

\int_{1}^{\infty} \frac{2}{x ^{5}} d x

integral from 0 to 2pi of sin^2(1/3 θ)

\int_{0}^{2 π} sin^{2} (\frac{1}{3} θ) d θ

Frequently Asked Questions (FAQ)

What is the integral from 0 to 6 of |x^2-4x| ?
The integral from 0 to 6 of |x^2-4x| is 64/3