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Find the area bounded by the x-axis, par...

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

Text Solution

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The correct Answer is:
`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)`
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