Solve P _ { f } ( t ) = ∫ (t^2+20)dt=t^3/3+20t+C

$$P _ { f } ( t ) = \int ( t ^ { 2 } + 20 ) d t = \frac { t ^ { 3 } } { 3 } + 20 t + C$$

Solve for C

$$C=С$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$3\int t^{2}+20\mathrm{d}t=t^{3}+60t+3C$$

Swap sides so that all variable terms are on the left hand side.

$$t^{3}+60t+3C=3\int t^{2}+20\mathrm{d}t$$

Subtract t^{3} from both sides.

$$60t+3C=3\int t^{2}+20\mathrm{d}t-t^{3}$$

Subtract 60t from both sides.

$$3C=3\int t^{2}+20\mathrm{d}t-t^{3}-60t$$

The equation is in standard form.

$$3C=С$$

Divide both sides by 3.

$$\frac{3C}{3}=\frac{С}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$C=\frac{С}{3}$$

Solve for t

$$t\in \mathrm{R}$$

$$C=С$$