Question

Find the area between the curves x=f(y) and x=g(y)

Answer 1

Step-by-step explanation:

Solution

Correct option is

A

9

Given curves are, y=

x

(i)

y=

2

x−3

(ii)

and x-axis i.e. y=0 (iii)

Now equation (i) is y

2

=x is right handed parabola but with positive values of y the part of the curve lying above x-axis

Now solving (i) & (ii) we get 4x=(x−3)

2

⇒ x

2

−10x+9=0 ⇒ (x−1)(x−9)=0

⇒ x=1,x=9, rejecting x=1 as it gives y=−1

∴ x=9,y=3

∴ Required area =∫

0

9

x

dx−∫

3

9

(

2

x−3

)dx

=18−9=9square units