Area bounded by the curves `4y = |x^2-4| and y + | x | = 7`, is equal to :

Options

A. 32
B. 16
C. 24
D. None of these

Answer

A

Explanation

`4y=|4-x^(2)|`
`implies{{:(4y=4-x^(2),:,-2lexle2),(4y=x^(2)-4,:,xlt-2" or "x gt2):}`
`y=7-|x|`
`implies" "y={(7+x:xlt0),(7-x:xge0):}`
Solving, `4y=x^(2)-4" and "y=7-x`, we get x = 3.
The curves are symmetrical about Y-axis.

Therefore, required area
`=2{int_(0)^(2)(7-x-(1)/(4)(4-x^(2)))dx+int_(2)^(3)[7-x-(1)/(4)(x^(2)-4)]}dx`
= 32 sq units