Question

The area between x=y² and x=4 is divided into two equal parts by the line x=a, find the value of a.

Answer 1

The line,x=a,divides the area bounded by the parabola and x=4 into two equal

parts.

∴Area OAD=Area ABCD

It can be observed that the given area is symmetrical about x-axis.

⇒Area OED=Area EFCD

Area OED=∫a0ydx

=∫a0√xdx

=[x3/2/3/2]a0

=2/3(a)3/2...(1)

Area of EFCD=∫40√xdx

=[x3/2/3/2]40

=2/3[8-a3/2]...(2)

From (1)and(2),we obtain

2/3(a)3/2=2/3[8-(a)3/2]

⇒2.(a)3/2=8

⇒(a)=3/2=4

⇒(a)=(4)2/3

Therefore,the value of a is (4)2/3.