1. ## Integral Type Problem

Find the value of k to the nearest integer such that the line x=k divides the area under f(x)=(x^3)/36 - x + 15 on [0,20] into two equal areas.

I set up an integral with the integrand being the f(x) from 0 to 20 and I got 1,211.11 then I divided by two which is 605.556. I am not quite sure what to do from here. Can someone shed some light on this problem? Thanks!

2. $\int_0^k f(x) \, dx = \frac{1}{2} \int_0^{20} f(x) \, dx$

$\frac{k^4}{144} - \frac{k^2}{2} + 15k = \frac{1}{2} \int_0^{20} f(x) \, dx$

solve for k