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

### Chapter: 21. Areas of Bounded Regions

#### Subject: Maths - Class 12th

##### Q. No. 32 of Exercise 21.3

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

32
##### Find the area bounded by the curves x = y2 and x = 3 – 2 y2.

To find area bounded by

X = y2 …(i)

And

X = 3 – 2y2 …(ii)

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

y2 = 3 – 2y2

Or 3y2 = 3

Or y = 1

When y = 1 then x = 1 and when y = – 1 then x = 1

Equation (i) represents an upward parabola with vertex (0, 0) and axis – y.

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

They intersect at A (1, – 1) and C (1, 1)

These are shown in the graph below: -

Required area = Region OABCO

= 2 Region OBCO

= 2[Region ODCO + Region BDCB]

The area bounded by the curves x = y2 and x = 3 – 2 y2 is

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52