What's the area bounded together by the equations; y=#x^2# and y=mx ?

1 Answer
Dec 11, 2017

#abs(m^3)/6#

Explanation:

#y=x^2# and #y=mx# intersect at #0# and at #m#.

For positive #m#, we have:
For all #x# in #(0,m)#, x^2 < mx#, so the area is

#int_0^m (mx-x^2) dx = [(mx^2)/2-x^3/3]_0^m#

# = m^3/6#

For negative #m#, the area is the same as the area for #absm# by symmetry. So we have Area = #-m^3/6# for #m < 0#

We can combine the two answers as: #A = abs(m^3)/6#