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8

The area between x = y^{2} and x = 4 is divided into two equal parts by the line x = a, find the value of a.

It is given that the area between x = y^{2} and x = 4 is divided into two equal parts by the line x = a.

Thus, Area OAD = Area ABCD

Now, we can observed that the given area is symmetrical about x-axis.

⇒ Area OED = Area EFCD

Now, Area of OED =

Area of EFCD =

Therefore, from equations (1) and (2), we get,

Hence, the required value of a is .

8

1

Find the area of the region bounded by the curve y^{2} = x and the lines x = 1, x = 4 and the x-axis in the first quadrant.