



 
Hi James, y = 3x  5x^{2} = x(3  5x) crosses the xaxis at x = 0 and x = 5/3 so find the area of the region bounded by y = 3x  5x^{2} and the xaxis by integrating 3x  5x^{2} from x = 0 to x = 5/3. Call the value A. Suppose the line through the prigin y = mx intersects the parabola at Q with xcoordinate p. The task is to find m so that Evaluation of the integral gave me
The relationship between p and m comes from the fact that the point Q is on the line y = mx and also on the parabola y = 3x  5x^{2}. Thus mp = 3p  5p^{2} or p = (3  m)/5. Substitute into (1) to get
Solve for m. Harley  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 