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

### Chapter: 21. Areas of Bounded Regions

#### Subject: Maths - Class 12th

##### Q. No. 39 of Exercise 21.3

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39
##### Make a sketch of the region{(x,y): 0 ≤ y ≤ x2 + 3; 0 ≤ y ≤ 2x + 3; 0 ≤ x ≤ 3} and find its area using integration.

To find area given equations are

Y = x2 + 3 …(i)

Y = 2x + 3 …(ii)

And x = 3 …(iii)

Solving the above three equations to get the intersection points,

x2 + 3 = 2x + 3

Or x2 – 2x = 0

Or x(x – 2) = 0

And x = 0 or x = 2

y = 3 or y = 7

Equation (1) represents a parabola with vertex (3, 0) and axis as y – axis.

Equation (2) represents a line a passing through (0, 3) and ( – 3/2, 0)

The points of intersection are A (0,3) and B(2,7).

These are shown in the graph below:

Required area =

The area of the region{(x,y): 0yx2 + 3; 0 y 2x + 3; 0 x 3} is

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