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anonymous

  • 5 years ago

Help with integration with polar coordinates? The main problem I'm having is finding the bounds in polar coordinates. The problem is: Integration of 3sqrt(x^2+y^2)dydx from 0 to sqrt(4-x^2) and from -2 to 2. If someone would tell me how to convert the bounds to polar coordinates, that would be great because I know the integrand converted is 3sqrt(r^2)

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  1. anonymous
    • 5 years ago
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    do you know the answer? final answer?

  2. anonymous
    • 5 years ago
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    answer choices: a) 18 b) 15pi/2 c) 8pi d) 4pi e) none of the above but I don't know the final answer.

  3. anonymous
    • 5 years ago
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    hmmmmm let me check my working first. are you 2nd year?

  4. anonymous
    • 5 years ago
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    3rd year

  5. anonymous
    • 5 years ago
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    that was weird!

  6. anonymous
    • 5 years ago
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    my sister have this in her 2nd year, so idk if the problem in 3rd year is different.

  7. anonymous
    • 5 years ago
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    I got 16pi...

  8. anonymous
    • 5 years ago
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    no no, it's 8pi, answer is c

  9. anonymous
    • 5 years ago
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    thank you, but can you tell me how to convert the bounds or how you got the answer?

  10. anonymous
    • 5 years ago
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    okay, theta bound: y bounds from y=0 to y=sqrt(4-x^2) <-> x^2+y^2=4=2^2 which is the equation of circle center (0,0) radius 2 so if you draw this on paper, you'll se y bounds from y=0 to upper hafl of the circle. then you can see theta run from 0 to pi 0<=theta<=pi

  11. anonymous
    • 5 years ago
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    r bound: r runs from center (0,0) to circle x^2+y^2=4 so 0<=r<=2

  12. anonymous
    • 5 years ago
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    so: omega={ (r,theta): 0 <= r <=2, 0 <= theta <= pi } then do the integration.

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