The problem is stated as "Find m such that the area of the region bounded by y = mx and y = x^2 - 1 is equal to 36."
I tried solving it by systems of equations:
mx = x^2 - 1 (1)
and the second equation being the integral of [mx - (x^2 - 1)]dx = 36 which gave me:
(mx^2)/2 - (x^3)/3 + x = 36 (2)
then trying to simplify (1) and (2).
Is this the correct way of solving the problem or is there an easier way to solve it. Thanks.
These are not two simultaneous equations. The two solutions to (1) (if they exist) will give you the bounds of the integral. Then you integrate with those bounds (which ought to remove $x$ completely), and set that equal to $36$.