InterviewSolution
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InterviewSolution
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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` |
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Answer» Correct Answer - `4 " sq. units ; "a=2sqrt(2)` `"Given "y=1+(8)/(x^(2))`. Here y is always positive, hence, curve is lying above the a-axis. `therefore" Req. area "=int_(2)^(4)ydx=int_(2)^(4)(1+(8)/(x^(2)))dx` `=[x-(8)/(x)]_(2)^(4)=4.` If x=a bisects the area, then we have `overset(a)underset(2)int(1+(8)/(x^(2)))dx=[x-(8)/(x)]_(2)^(a)=[a-(8)/(a)-2+4]=(4)/(2).` `"or "a-(8)/(a)=0` `"or "a^(2)=8` `"or "a=pm2sqrt(2)` `"Since "agt2,a=2sqrt(2).` |
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