Question

For what values of m, the area of the region bounded by the curves y = x – x² and the line y = mx equals 9/2? 

(a) – 4 

(b) –2 

(c) 2 

(d) 4

Answer 1

Answer is (b) -2 and (d) 4

Case-I: When m < 0

Area of the region

= (1/6) (1 – m)

Also, it is given that,

(1/6) (1 – m)³ = 9/2  

(1 – m)³ = 27

(1 – m) = 3

m = – 2.

Case II: When m > 0

Area of the region

= – (1/6) (1 – m)³ 

It is also given that 

- (1/6) (1 – m)³ = 9/2 

(1 – m)³ = – 27 

1 – m = – 3  

m = 4