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

The integral from 2x to x^2 of sqrt(t) is (2x^3-4sqrt(2)x^{3/2})/3

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integral from 2x to x^2 of sqrt(t)

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

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

Solution steps

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

Apply the Power Rule

: [\frac{2}{3} t^{\frac{3}{2}}]_{2 x}^{x^{2}}

= [\frac{2}{3} t^{\frac{3}{2}}]_{2 x}^{x^{2}}

Compute the boundaries:

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

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

Simplify

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

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What is the integral from 2x to x^2 of sqrt(t) ?
The integral from 2x to x^2 of sqrt(t) is (2x^3-4sqrt(2)x^{3/2})/3