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anonymous

  • 5 years ago

what is the best way to solve a double integral question without drawing the figure we need to integrate over?

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  1. amistre64
    • 5 years ago
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    guessing lol

  2. amistre64
    • 5 years ago
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    havent tried doubles yet....

  3. anonymous
    • 5 years ago
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    lol.. but you said you were guessing..

  4. amistre64
    • 5 years ago
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    whats the function or functions to double integrate :)

  5. anonymous
    • 5 years ago
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    yeah giv us the function..

  6. amistre64
    • 5 years ago
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    and make it a hard one lol

  7. amistre64
    • 5 years ago
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    something with an exponent of 3 in it ;)

  8. amistre64
    • 5 years ago
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    and a negative

  9. anonymous
    • 5 years ago
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    let it be a double integral of 4xy-y^3 over the area bounded by the curves y=x^2 n y=x^(1/2)

  10. amistre64
    • 5 years ago
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    if we do the x we get......umm........how do we do doubles anyways?

  11. amistre64
    • 5 years ago
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    is this confined to a single plane right?

  12. amistre64
    • 5 years ago
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    i see the football shape made by the bounds of x^2 and sqrt(x)

  13. anonymous
    • 5 years ago
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    the region bounded by those curves looks like a rugby ball..

  14. amistre64
    • 5 years ago
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    dunno what to do with the 4xy-y^3 function tho..... how does that come into play?

  15. amistre64
    • 5 years ago
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    if we int with respect to y it goes; 2xy^2-y^4/4 right?

  16. amistre64
    • 5 years ago
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    and with respect to x its: 4yx^3/3 +xy^3 ??

  17. anonymous
    • 5 years ago
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    the major problem n which also the 1st step is to find the limits for the double integral for individual x and y.. once u r able to get that.. then its more or less like normal integration..

  18. anonymous
    • 5 years ago
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    how hard is it to find limits solve sqrt(x) = x^2

  19. anonymous
    • 5 years ago
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    x^4 = x x(x^3 -1) =0 x=0, x=1 for real solutions

  20. anonymous
    • 5 years ago
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    when x=0 , y= 0 when x=1, y= 1

  21. anonymous
    • 5 years ago
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    so its just \[\int\limits_{0}^{1}\int\limits_{0}^{1} f(x,y) dx dy \]

  22. anonymous
    • 5 years ago
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    doesnt matter which order u integrate, in the above I do x first

  23. anonymous
    • 5 years ago
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    so f(x,y) = 4xy-y^3 int f dx = 2x^2 y -xy^3 [ from x=1..x=0] = ( [2y -y^3 ] - [0] ) = 2y -y^3 now we integrate that with respect to y , from y=0 to y=1

  24. anonymous
    • 5 years ago
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    so we get [ y^2 -y^4 / 4 ] from y=1..y=0 = 1- (1/4) = 3/4 //final answer

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