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

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

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

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

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

Decimal

1.78104 \dots

Solution steps

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

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

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

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

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