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