What is the integral from 0 to sin(x) of 2sqrt(t) ?

The integral from 0 to sin(x) of 2sqrt(t) is 4/3 sin^{3/2}(x)

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integral from 0 to sin(x) of 2sqrt(t)

\int_{0}^{s i n (x)} 2 t d t

\frac{4}{3} sin^{\frac{3}{2}} (x)

Solution steps

\int_{0}^{s i n (x)} 2 t d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{0}^{s i n (x)} t d t

Apply the Power Rule

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

Compute the boundaries:

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

= 2 \cdot \frac{2}{3} sin^{\frac{3}{2}} (x)

Simplify

= \frac{4}{3} sin^{\frac{3}{2}} (x)

What is the integral from 0 to sin(x) of 2sqrt(t) ?
The integral from 0 to sin(x) of 2sqrt(t) is 4/3 sin^{3/2}(x)