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Title : Oct 17-8:44 PM (Page 1 of 11)

Title : Oct 17-9:03 PM (Page 2 of 11)shatalov/cn_13_3.pdf · Title : Oct 20-3:29 PM (Page 11 of 11) FACT: If f (x, y) > C) and f is continuous on the region D then the volume V of

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Page 1: Title : Oct 17-9:03 PM (Page 2 of 11)shatalov/cn_13_3.pdf · Title : Oct 20-3:29 PM (Page 11 of 11) FACT: If f (x, y) > C) and f is continuous on the region D then the volume V of

Title : Oct 17-8:44 PM (Page 1 of 11)

Page 2: Title : Oct 17-9:03 PM (Page 2 of 11)shatalov/cn_13_3.pdf · Title : Oct 20-3:29 PM (Page 11 of 11) FACT: If f (x, y) > C) and f is continuous on the region D then the volume V of

Title : Oct 17-9:03 PM (Page 2 of 11)

Page 3: Title : Oct 17-9:03 PM (Page 2 of 11)shatalov/cn_13_3.pdf · Title : Oct 20-3:29 PM (Page 11 of 11) FACT: If f (x, y) > C) and f is continuous on the region D then the volume V of

Title : Oct 17-9:03 PM (Page 3 of 11)

Page 4: Title : Oct 17-9:03 PM (Page 2 of 11)shatalov/cn_13_3.pdf · Title : Oct 20-3:29 PM (Page 11 of 11) FACT: If f (x, y) > C) and f is continuous on the region D then the volume V of

Title : Oct 17-9:07 PM (Page 4 of 11)

Page 5: Title : Oct 17-9:03 PM (Page 2 of 11)shatalov/cn_13_3.pdf · Title : Oct 20-3:29 PM (Page 11 of 11) FACT: If f (x, y) > C) and f is continuous on the region D then the volume V of

Title : Oct 17-9:09 PM (Page 5 of 11)

Page 6: Title : Oct 17-9:03 PM (Page 2 of 11)shatalov/cn_13_3.pdf · Title : Oct 20-3:29 PM (Page 11 of 11) FACT: If f (x, y) > C) and f is continuous on the region D then the volume V of

Title : Oct 17-9:10 PM (Page 6 of 11)

Page 7: Title : Oct 17-9:03 PM (Page 2 of 11)shatalov/cn_13_3.pdf · Title : Oct 20-3:29 PM (Page 11 of 11) FACT: If f (x, y) > C) and f is continuous on the region D then the volume V of

Title : Oct 17-9:10 PM (Page 7 of 11)

Page 8: Title : Oct 17-9:03 PM (Page 2 of 11)shatalov/cn_13_3.pdf · Title : Oct 20-3:29 PM (Page 11 of 11) FACT: If f (x, y) > C) and f is continuous on the region D then the volume V of

Solution: First sketch the region D.

Rewrite the given curves whih are given as y=y(x) in the form x=x(y).

We have

Since x is nonnegative we choose

Also we have

Title : Oct 17-9:11 PM (Page 8 of 11)

Page 9: Title : Oct 17-9:03 PM (Page 2 of 11)shatalov/cn_13_3.pdf · Title : Oct 20-3:29 PM (Page 11 of 11) FACT: If f (x, y) > C) and f is continuous on the region D then the volume V of

Title : Oct 17-9:11 PM (Page 9 of 11)

Page 10: Title : Oct 17-9:03 PM (Page 2 of 11)shatalov/cn_13_3.pdf · Title : Oct 20-3:29 PM (Page 11 of 11) FACT: If f (x, y) > C) and f is continuous on the region D then the volume V of

Title : Oct 20-3:28 PM (Page 10 of 11)

Page 11: Title : Oct 17-9:03 PM (Page 2 of 11)shatalov/cn_13_3.pdf · Title : Oct 20-3:29 PM (Page 11 of 11) FACT: If f (x, y) > C) and f is continuous on the region D then the volume V of

Title : Oct 20-3:29 PM (Page 11 of 11)