Find the area bounded by the x-axis, part of the curve `y=(1-8/(x^2))` , and the ordinates at `x=2a n dx=4.` If the ordinate at `x=a` divides the area into two equal parts, then find `adot`

Options

A. `sqrt(2)` sq units
B. `2sqrt(2)` sq units
C. `3sqrt(2)` sq units
D. None of these

Answer

B

Explanation

Area `=int_(2)^(4)(1+(8)/(x^(2)))dx`

Since, the ordinate x = a divides area into two equal parts, therefore
`int_(2)^(a)(1+(8)/(x^(2)))dx=(1)/(2)int_(2)^(4)(1+(8)/(x^(2)))dx`
`rArr[x-(8)/(x)]_(2)^(a)=(1)/(2)[x-(8)/(x)]_(2)^(4)`
`rArr(a-(8)/(a))-(2-4)=(1)/(2)[(4-2)-(2-4)]`
`rArra-(8)/(a)+2=2rArra=sqrt(8)=2sqrt(2)` sq units