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}

\int_{- 2}^{2} x^{3} cos (\frac{x}{2}) + \frac{1}{2} 4 - x^{2} d x

\int_{0}^{\frac{π}{2}} 2 cos (t) d t

\int_{\frac{1}{2}}^{x} \frac{2}{t ^{2}} d t

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

\int_{0}^{3} x e^{- 0.4 x} d x

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