What is the integral from 0 to sin(θ) of θr ?

The integral from 0 to sin(θ) of θr is (θsin^2(θ))/2

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integral from 0 to sin(θ) of θr

\int_{0}^{s i n (θ)} θ r d r

\frac{θ sin ^{2} ( θ )}{2}

Solution steps

\int_{0}^{s i n (θ)} θ r d r

Take the constant out:

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

= θ \cdot \int_{0}^{s i n (θ)} r d r

Apply the Power Rule

: [\frac{r ^{2}}{2}]_{0}^{s i n (θ)}

= θ [\frac{r ^{2}}{2}]_{0}^{s i n (θ)}

Compute the boundaries:

\frac{sin ^{2} ( θ )}{2}

= θ \frac{sin ^{2} ( θ )}{2}

Simplify

= \frac{θ sin ^{2} ( θ )}{2}

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What is the integral from 0 to sin(θ) of θr ?
The integral from 0 to sin(θ) of θr is (θsin^2(θ))/2