What is the integral from 0 to 2 of |x^2-sqrt(x)| ?

The integral from 0 to 2 of |x^2-sqrt(x)| is 8/3-(4sqrt(2)-2)/3

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integral from 0 to 2 of |x^2-sqrt(x)|

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

\frac{8}{3} - \frac{4 2 - 2}{3}

Decimal

1.44771 \dots

Solution steps

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

Eliminate Absolutes

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

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

\int_{1}^{2} x^{2} - x d x = \frac{7}{3} - \frac{4 2 - 2}{3}

= \frac{1}{3} + \frac{7}{3} - \frac{4 2 - 2}{3}

Combine the fractions

\frac{1}{3} + \frac{7}{3} : \frac{8}{3}

= \frac{8}{3} - \frac{4 2 - 2}{3}

x \to 5 lim (5 x - (x - 5))

n = 1 \sum \infty e^{- \frac{9 n}{2}}

\int - 2 e^{- 2 x} sin (- 2 y)

f (x) = x^{4} + \frac{2}{x}

n = 0 \sum \infty \frac{n}{n ^{2} + 9}

What is the integral from 0 to 2 of |x^2-sqrt(x)| ?
The integral from 0 to 2 of |x^2-sqrt(x)| is 8/3-(4sqrt(2)-2)/3