What is the integral from 0 to 1+cos(θ) of r ?

The integral from 0 to 1+cos(θ) of r is ((cos(θ)+1)^2)/2

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integral from 0 to 1+cos(θ) of r

\int_{0}^{1 + c o s (θ)} r d r

\frac{( cos ( θ ) + 1 ) ^{2}}{2}

Solution steps

\int_{0}^{1 + c o s (θ)} r d r

Apply the Power Rule

: [\frac{r ^{2}}{2}]_{0}^{1 + c o s (θ)}

= [\frac{r ^{2}}{2}]_{0}^{1 + c o s (θ)}

Compute the boundaries:

\frac{( cos ( θ ) + 1 ) ^{2}}{2}

= \frac{( cos ( θ ) + 1 ) ^{2}}{2}

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What is the integral from 0 to 1+cos(θ) of r ?
The integral from 0 to 1+cos(θ) of r is ((cos(θ)+1)^2)/2