Yahoo Answers: Answers and Comments for Calculus I homework question? [Mathematics]
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From hey
enUS
Tue, 23 Jul 2019 09:34:03 +0000
3
Yahoo Answers: Answers and Comments for Calculus I homework question? [Mathematics]
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https://answers.yahoo.com/question/index?qid=20190723093403AAILOVj
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From Mike G: V =
3
∫ πy^2 dx = ∫π*49(64x^2 dx [1,3]
1
= ...
https://answers.yahoo.com/question/index?qid=20190723093403AAILOVj
https://answers.yahoo.com/question/index?qid=20190723093403AAILOVj
Tue, 23 Jul 2019 10:33:38 +0000
V =
3
∫ πy^2 dx = ∫π*49(64x^2 dx [1,3]
1
= π[3136x49x^3/3] [1,3]
= π([3136*39*49]  [313649/3])
= π(89673136+49/3)
17542π/3

From Ian H: This might help you to see how to set up the i...
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https://answers.yahoo.com/question/index?qid=20190723093403AAILOVj
Tue, 23 Jul 2019 10:52:52 +0000
This might help you to see how to set up the integral.
An element of volume is created by rotating a rectangle y*dx around x axis.
That volume element will be coin shaped looked at edge on, although usually called a disc, and should be seen as a stubby cylinder with volume like πr^2*h.
πr^2 = πy^2, and the height/depth h is taken as dx for an element of volume.
Since y^2 = 49(64 – x^2), the integrand becomes 49π(64 – x^2)dx
The x limits go from 1 to 3, so you get
V = {x: 1 to 3} 49π∫(64 – x^2)dx
You should find ∫(64 – x^2)dx quite easy
it is 64x – x^3/3, so applying those limits
V = 49π[192 – 9 – (64 – 1/3)] = 49π *359/3 = 17542π/3 ~ 18369.9

From RealPro: Have you not been taught the method of disks a...
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https://answers.yahoo.com/question/index?qid=20190723093403AAILOVj
Tue, 23 Jul 2019 09:55:18 +0000
Have you not been taught the method of disks and washers?
The area of some disk is pi [ (7sqrt(64 − x^2))^2  0^2 ] so that's what we will integrate
pi * int[1 to 3] 49(64x^2) dx
= ?