Area under the curveHard
Question
For which of the following values of m, is the area of the region bounded by the curve y = x - x2 and the line y = mx equals to 9/2 ?
Options
A.-4
B.-2
C.2
D.4
Solution
The two curves meet at
mx = x - x2 or x2 = x(1 - m) ∴ x = 0,1 - m
(y1 - y2)dx = 
(x - x2 - mx)dx = 
=
if m < 1
or (1-m)3
or (1 m)3 = 27
∴ m = - 2
But if m > 1 then 1 - m is negative, then
-(1 - m)3
∴ - (1 - m)3 = - 27or1- m = - 3 ∴ m = 4
mx = x - x2 or x2 = x(1 - m) ∴ x = 0,1 - m
(y1 - y2)dx = (x - x2 - mx)dx = =
if m < 1or (1-m)3
or (1 m)3 = 27 ∴ m = - 2
But if m > 1 then 1 - m is negative, then
-(1 - m)3
∴ - (1 - m)3 = - 27or1- m = - 3 ∴ m = 4
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