UPSC NDA I and II 2020 Math Solved Paper

Two given graphs are y2=2x and y=x.
Point of intersections are :
x2=2x⇒x2−2x=0
x(x−2)=0
x=0 and 2&y=0 and 2
So, points of intersections are (0,0) and (2,2) . The graph are The required area is the shaded portion
A=|

2

∫

0

(y1−y2).dx| =|

2

∫

0

(√2x−x).dx| =[

2√2(x) 3 2

3

−

x2

2

]02
=

2√2

3

(2)

3

2

−2 =

8

3

−2=

2

3