What is the integral from 0 to tan(x) of sqrt(t) ?

The integral from 0 to tan(x) of sqrt(t) is 2/3 tan^{3/2}(x)

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integral from 0 to tan(x) of sqrt(t)

\int_{0}^{t a n (x)} t d t

\frac{2}{3} tan^{\frac{3}{2}} (x)

Solution steps

\int_{0}^{t a n (x)} t d t

Apply the Power Rule

: [\frac{2}{3} t^{\frac{3}{2}}]_{0}^{t a n (x)}

= [\frac{2}{3} t^{\frac{3}{2}}]_{0}^{t a n (x)}

Compute the boundaries:

\frac{2}{3} tan^{\frac{3}{2}} (x)

= \frac{2}{3} tan^{\frac{3}{2}} (x)

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What is the integral from 0 to tan(x) of sqrt(t) ?
The integral from 0 to tan(x) of sqrt(t) is 2/3 tan^{3/2}(x)