There is a line through the origin that divides the region bounded by the parabola y = 2x − 7 x^2 and the x-axis into two regions with equal area. What is the slope of that line?

Answer 1

If you look through previous solved problems, there is a problem exactly like this one solved by Jim S. afe days ago.

The area in question runs from x = 0 to x = 7/2.

Calculate the area under the parabola on this interval.

Then the most important trick is to find the intersection of y=mx (a line through the origin) and the parabola.

Then evaluate the integral from x=0 to the point of intersection of 2x-7x²-x; this will be a function of m.

Set this function equal to 1/2 the area under the parabola.

Solve for m. Please note that the function of m may be a cubic which you will need to solve graphically.