Question

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`

Answer 1

Correct Answer - `2sqrt(2)`
Here, `int_(2)^(a)(1+(8)/(x^(2))) dx = int_(a)^(4)(1+(8)/(x^(2))) dx`
`rArr [x-(8)/(x)]_(2)^(a) = [x-(8)/(x)]_(a)^(4)`
`rArr (a-(8)/(a))-(2-4)=(4-2)-(a-(8)/(a))`
`rArr a-(8)/(a) +2=2-a+(8)/(a) rArr 2a-(16)/(a) =0`
`rArr 2(a^(2) -8)=0`
`rArr a=pm 2sqrt(2) " " `[neglecting -ve sign]
`therefore a=2sqrt(2)`