What is the integral from 1 to 2 of x^2-sqrt(x) ?

The integral from 1 to 2 of x^2-sqrt(x) is 7/3-(4sqrt(2)-2)/3

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integral from 1 to 2 of x^2-sqrt(x)

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

\frac{7}{3} - \frac{4 2 - 2}{3}

Decimal

1.11438 \dots

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

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

What is the integral from 1 to 2 of x^2-sqrt(x) ?
The integral from 1 to 2 of x^2-sqrt(x) is 7/3-(4sqrt(2)-2)/3