# integration problem

• March 23rd 2010, 03:47 AM
mastermin346
integration problem
Given that $\frac{dp}{dt}=kt^2$ where k is constant.Given also $p=\frac{11}{3}$ and $\frac{dp}{dt}=-2$ when $t=-2.$Express $p$ in term of $t$
• March 23rd 2010, 04:03 AM
Given that $\frac{dp}{dt}=kt^2$ where k is constant.Given also $p=\frac{11}{3}$ and $\frac{dp}{dt}=-2$ when $t=-2.$Express $p$ in term of $t$
$\frac{dp}{dt}=kt^2\ \Rightarrow\ p=\frac{k}{3}t^3+C$
$\frac{dp}{dt}=-2\ for\ t=-2\ \Rightarrow\ k(-2)^2=-2\ \Rightarrow\ 4k=-2$
$\frac{11}{3}=\left(-\frac{1}{2}\right)\left(\frac{1}{3}\right)(-2)^3+C$