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

The integral from 0 to 4 of |x^2-sqrt(x)| is 50/3

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integral from 0 to 4 of |x^2-sqrt(x)|

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

\frac{50}{3}

Decimal

16.66666 \dots

Solution steps

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

Eliminate Absolutes

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

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

\int_{1}^{4} x^{2} - x d x = \frac{49}{3}

= \frac{1}{3} + \frac{49}{3}

Simplify

\frac{1}{3} + \frac{49}{3} : \frac{50}{3}

= \frac{50}{3}

\int_{0}^{2} 2 π (2 - x) (2 x - x^{2}) d x

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

\int_{0}^{1} y sin (1) d y

\int_{0}^{x} sin (2 x) d x

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

What is the integral from 0 to 4 of |x^2-sqrt(x)| ?
The integral from 0 to 4 of |x^2-sqrt(x)| is 50/3