What is the area bounded by the curve `y = x^(2)` and the line `y = 16` ?

Options

A. `32//3`
B. `64//3`
C. `256//3`
D. `128//3`

Answer

C

Explanation

Given equations of curves are
`y = x^(2) "………"(i)`
and `y = 16 "………"(ii)`
On solving Eqs. (i) and (ii) , we get
`x^(2) = 16 rArr x = 4 , -4`
`:.` Points of intersectoin are `(4,16)` and `(-4,16)`.

Required area `= int_(-4)^(4)(16-x^(2)) dx = 2int_(0)^(4) (16-x^(2)) dx`
`= 2[16x-(x^(3))/(3)]_(0)^(4) = 2[64-64/3] = 2 xx 64 xx 2/3`
`= (256)/(3)` sq unit