What is the integral from 0 to sin(x) of 4sqrt(t) ?

The integral from 0 to sin(x) of 4sqrt(t) is 8/3 sin^{3/2}(x)

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integral from 0 to sin(x) of 4sqrt(t)

\int_{0}^{s i n (x)} 4 t d t

\frac{8}{3} sin^{\frac{3}{2}} (x)

Solution steps

\int_{0}^{s i n (x)} 4 t d t

Take the constant out:

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

= 4 \cdot \int_{0}^{s i n (x)} t d t

Apply the Power Rule

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

= 4 [\frac{2}{3} t^{\frac{3}{2}}]_{0}^{s i n (x)}

Compute the boundaries:

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

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

Simplify

= \frac{8}{3} sin^{\frac{3}{2}} (x)

\int sin^{5} (x co) s^{5} x d x

7 x (x + 5 y) (\frac{d y}{d x}) = 7 y (x - 5 y)

\frac{1}{s ( s ^{2} + 36 )}

(4 x + 4 y)^{3} = 64 x^{3} + 64 y^{3}, (- 1, 1)

\frac{d}{d x} (- \frac{49 x}{36 y})

What is the integral from 0 to sin(x) of 4sqrt(t) ?
The integral from 0 to sin(x) of 4sqrt(t) is 8/3 sin^{3/2}(x)