Solve ∫ 10^2r^2+r^2dvarphi

$$\int 10 ^ { 2 } r ^ { 2 } + r ^ { 2 } d \varphi$$

Evaluate

$$101\phi r^{2}+С$$

Solution Steps

Find the integral of 10^{2}r^{2}+r^{2} using the table of common integrals rule \int a\mathrm{d}\phi =a\phi .

$$\left(10^{2}r^{2}+r^{2}\right)\phi$$

Simplify.

$$101r^{2}\phi$$

If F\left(\phi \right) is an antiderivative of f\left(\phi \right), then the set of all antiderivatives of f\left(\phi \right) is given by F\left(\phi \right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$101r^{2}\phi +С$$

Differentiate w.r.t. r

$$202r\phi$$