Question

Find the volume of the solid generated by the revolution of the area bounded by the parabola y2=4x and the line 4x-3y=0,about the y-axis
​

Answer 1

y

2

=4x⇒x=

4

y

2

2x−3y+4=0⇒x=

2

3

y−2

4

y

2

=

2

3

y−2

y

2

=6y−8

y

2

−6y+8=0

(y−4)(y−2)=0

y

1

=2,y

2

=4

A=∫

2

4

(

2

3

y−2)−(

4

y

2

)dy

=[

4

3y

2

−2y−

12

y

3

]

2

4

=

3

36−24−16−9+12+2

=

3

1

sq. units