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anonymous

  • 5 years ago

Hi, can someone please help me with this. I really appreciate it. Given the sum of two iterated integrals I = 0∫(√2)/2 0 ∫x √(x2 + y2) dydx + (√2)/2 ∫1 0 ∫√1-x^2) √(x2 + y2) dydx a) use the set notation to describe the region D of integration b) sketch region D I think I have a general idea, but I'm unsure. Do I set the intervals of dy and dx equal to each other? Thanks again.

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  1. anonymous
    • 5 years ago
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    Don't understand your notation: what is the 0s in front of integral sign?

  2. anonymous
    • 5 years ago
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    My bad. I'll rewrite it.

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  3. anonymous
    • 5 years ago
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    The first one seems to be describing the line y=x

  4. anonymous
    • 5 years ago
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    The whole region is a semicircle of radius one, pierced by y=x

  5. anonymous
    • 5 years ago
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    Thanks, but i"m still lost. What would the interval of the region be?

  6. anonymous
    • 5 years ago
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    First one 0<y<x 0<x<(sq rt 2)/2

  7. anonymous
    • 5 years ago
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    Second one 0<y<sq rt (1-x^2) (sq rt2)/2<x<1

  8. anonymous
    • 5 years ago
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    Oh, so I don't have to write a notation that combines the two iterated integrals as one?

  9. anonymous
    • 5 years ago
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    I was just 'quoting' what the integrals say to answer your question, I wasn't working on the problem so to speak.

  10. anonymous
    • 5 years ago
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    The first one describes a region that looks like a piece of pie between 0 and y=x of length (sq rt 2)/2. And the second part goes from the end of that starting at (sq rt 2)/2 to 1 a sector of a semicircle.

  11. anonymous
    • 5 years ago
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    Okay, thanks a lot!

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