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Find the area of the domain D which is in the first quadrant?

Find the area of the domain D which is in the first quadrant and bounded by xy=1, xy=3, y=x, y=3x.

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George C. | Humboldt State and Georgetown graduateHumboldt State and Georgetown graduate
5.0 5.0 (2 lesson ratings) (2)
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You must paramaterize.  It is easiest if you draw a picture.

 

[(1/3)^(1/2), 1 ] int (3x - 1/x)dx  +  [1, (3)^(1/2)] int (3/x  -  x)dx

 

(3/2 x^2 - ln x) [(1/3)^(1/2), 1 ]  +  (3 ln x  -  (x^2/2) [1, (3)^(1/2)]

 

Performing the arithmetic gives ln 3

 

A = ln 3