AMU Engineering 2017 solved paper Solved Paper

Given curves are
y=2x−x2 .......(i)
y=−x .......(ii)
On solving Eqs. (i) and (ii) we get,
−x=2x−x2
⇒ x2−3x=0⇒x(x−3)=0
⇒ x=0 or x=3
The area ( A ) bounded by the curve is the shaded region shown in the figure.
Now, A=

3

∫

0

[(2x−x2)−(−x)]dx =

3

∫

0

(−x2+3x)dx
=|

−x3

3

+

3x2

2

|03=

−1

3

(3)3+

3

2

(3)2
=−9+

27

2

=

9

2

sq units