Originally Posted by
radioheadfan There is a line through the origin that divides the region bounded by the parabola y=8x−4x2 and the x-axis into two regions with equal area. What is the slope of that line?
Well I integrated the fuction from zero to 2, and got 16/3. Took half the area. Integrated with mx, and got 2m.
You integrated mx...between what and what? This doesn't sound correct: it should have been between 0 and 2 -m/4 = the x-coordinate of the intersection point of the parabola and the line, and then you still need to add to this the integral from 2 - m/4 to 2 of the parabola!
This is a very nasty exercise, and the best I got is an awful cubic equation in m.
Tonio
Then set it equal to 16/6 and solving for m found the slope to be 4/3. My online hw says this is incorrect. How? and what's the actual answer?