MHTCET 2016 Math Solved Paper

(b) The equation of given curve is y = 2x - x2
⇒ x2 - 2 x = - y
⇒ x2 - 2 x + 1= - y + 1
⇒ (x−1)2 = - ( y - 1 )
Which is the equation of parabola whose vertex is (1,1) and it is open downward.

For intersection of theparabola with the X-axis, put y = 0, then we get
0 = 2x- x2
⇒ x(2 - x) = 0
⇒ x = 0 ,2
Hence, area of bounded region between the curve and X-axis
=

2

∫

0

ydx
=

2

∫

0

(2x−x2)dx = [

2x2

2

−

x3

3

]02
= [4−

8

3

−0−0]=

4

3

sq units.