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Compute the area of the region bounded by y=(17/4) - (1/x) and y=x.

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PaulRosandro | eNoter

Posted September 2, 2013 at 9:12 AM via web

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Compute the area of the region bounded by y=(17/4) - (1/x) and y=x.

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aruv | High School Teacher | Valedictorian

Posted September 2, 2013 at 9:29 AM (Answer #1)

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In graph red curve represent  `y=17/4-1/x`  and green line represents

y=x. These two graphs of curve and straight line intersect each other at point (4,4) and (1/4,1/4). We wish to find area bounded between these two curves.Let A be the required area

`A=int_(1/4)^4(17/4-1/x)dx-int_(1/4)^4 xdx`

`=int_(1/4)^4 (17/4-1/x-x)dx`

`=((17x)/4-ln(x)-x^2/2)_(1/4)^4`

`=(17-ln(4)-8)-(17/16-ln(1/4)-1/32)`

`=9-33/32-ln(4)-ln(4)`

`=255/32-2ln(4)`

`` Ans.

 

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