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robertr24
August 5th 2005, 04:26 PM
Hey all. I'm having a bit of a problem. In Dr. Ostazewski's manual, it's number 13 in practice exam 5. I'm confused about the area of integration. Since y >= x, I thought the area should have been x: (0 to w), y: (x to 1), and for the second part x: (w to sqrt w), y: (x to w/x)? In simpler terms, I thought the shaded region should be to the upper left of the line y = x instead of to the lower right. I don't get it. I would be more than grateful if someone could help me out. Thanks very much all.

krzysio
August 6th 2005, 12:44 AM
Dear Robertr24:

I do not know which edition of my manual you have: first or second edition, but
I think this is probably a typo that I have corrected in one of these posted errata:

First edition:
http://www.math.ilstu.edu/krzysio/P-Manual-Errata.pdf

Second edition:
http://www.math.ilstu.edu/krzysio/P-Manual-2ndEd-Errata.pdf

I hope this helps. If it does not, please reply, or send me an e-mail.

Yours most sincerely,
Krzys' Ostaszewski



Hey all. I'm having a bit of a problem. In Dr. Ostazewski's manual, it's number 13 in practice exam 5. I'm confused about the area of integration. Since y >= x, I thought the area should have been x: (0 to w), y: (x to 1), and for the second part x: (w to sqrt w), y: (x to w/x)? In simpler terms, I thought the shaded region should be to the upper left of the line y = x instead of to the lower right. I don't get it. I would be more than grateful if someone could help me out. Thanks very much all.

robertr24
August 6th 2005, 02:01 AM
Thanks. That clears things up a bit. However, I'm still confused about the actual integration. In the manual you have x:={0 to sqrt w}, y:={0 to x} for the first part, x:={sqrt w to 1}, y:={0 to x/w} for the second part. Doesn't this correspond to the area below the line y = x?

krzysio
August 6th 2005, 03:35 AM
The intersection of the line y = x and the hyperbola xy = w is at the point
( w^0.5, w^.05). First part is the integral over the shaded region between
the origin and the line y = w^.05, the second one is above that line
and still under the hyperbola. I still had typos in this solution, so I updated
the errata, and you can download corrected versions here:
http://www.math.ilstu.edu/krzysio/P-Manual-2ndEd-Errata.pdf
http://www.math.ilstu.edu/krzysio/P-Manual-Errata.pdf

Yours,
Krzys'


In the first part, we have


Thanks. That clears things up a bit. However, I'm still confused about the actual integration. In the manual you have x:={0 to sqrt w}, y:={0 to x} for the first part, x:={sqrt w to 1}, y:={0 to x/w} for the second part. Doesn't this correspond to the area below the line y = x?

robertr24
August 6th 2005, 12:17 PM
Thanks very much. I knew something was wrong there. It makes much more sense with the dx's and dy's interchanged. Sorry to drive you crazy. I will definitely look through ALL the errata before I post questions from now on. :)

krzysio
August 6th 2005, 12:39 PM
Dear Robert24:

Unfortunately, errors and typos still show up in my manuals, despite my best efforts.
So, I view your inquiry as a very nice gesture, helping me correct those errors. I appreciate it very much.

Yours very truly,
Krzys' Ostaszewski


Thanks very much. I knew something was wrong there. It makes much more sense with the dx's and dy's interchanged. Sorry to drive you crazy. I will definitely look through ALL the errata before I post questions from now on. :)