 ## Book: RD Sharma - Mathematics (Volume 2)

### Chapter: 21. Areas of Bounded Regions

#### Subject: Maths - Class 12th

##### Q. No. 22 of Exercise 21.3

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22
##### Prove that the area common to the two parabolas y = 2x2 and y = x2 + 4 is 32/3 sq. Units.

To find the area enclosed by,

y = 2x2 ...(i)

And y = x2 + 4 ...(ii)

On solving the equation (i) and (ii),

2x2 = x2 + 4

Or x2 = 4

Or x =  y = 8

Equation (1) represents a parabola with vertex (0,0) and axis as y - axis.

Equation (2) represents a parabola with vertex (0,4) and axis as the y - axis.

Points of intersection of parabolas are A(2,8) and B( – 2,8).

These are shown in the graph below: - Required area = Region AOBCA

= 2(Region AOCA)     Hence, proved that the area common to the two parabolas y = 2x2 and y = x2 + 4 is 32/3 sq. Units.

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