What is the area of the region bounded by the curve `f(x) = 1 - (x^(2))/(4), x in [-2,2]` , and the x-axis ?

Options

A. `8/3` sq unit
B. `4/3` sq unit
C. `2/3` sq unit
D. `1/3` sq unit

Answer

A

Explanation

Required area `= int_(-2)^(2) (1-(x^(2))/(4))dx`
Since, `(1-(x^(2))/(4))` is an even function therefore
`int_(-2)^(2) (1-(x^(2))/(4)) dx = 2int_(0)^(2) (1-(x^(2))/(4)) dx`
`= 2[x - (x^(3))/(12)]_(0)^(2) = 2[2-(2^(3))/(12)]`
`= 2(2-(2)/(3)) = 8/3` sq unit