anonymous
  • anonymous
Evaluate the following integrals by first reversing the order of integration. ∫(0,8)∫(y^(1/3),2) 8e^x^2 dxdy. Why is the limit when you reverse 0<=x<=2, 0<=y<=x^3 and not x^3<=y<=8?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
I'm confused with finding the limits for each when you reverse the order anyone got any tips?
TuringTest
  • TuringTest
drawing out the region of integration is almost always a good idea
TuringTest
  • TuringTest
|dw:1352232985691:dw|

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anonymous
  • anonymous
Yeah I got that too, but can't you say y^(1/3) to 8 is the limit? Go along the curve y=x^3 and stop at 8?
TuringTest
  • TuringTest
well what would the area between y^(1/3) and y=8 look like?
TuringTest
  • TuringTest
or rather x^3<=y<=8
anonymous
  • anonymous
ohh
anonymous
  • anonymous
it'd be the shaded area under y=8 but above y=x^3?
anonymous
  • anonymous
which we're not looking for right
TuringTest
  • TuringTest
|dw:1352233420315:dw|you got it :)
TuringTest
  • TuringTest
so in the area we want we want y bounded above by the function, not the line
anonymous
  • anonymous
it's so hard to see sometimes but got it thanks so much for your help!!
anonymous
  • anonymous
so whenever you want it bounded by the curve you'd take it from 0 to the curve?
TuringTest
  • TuringTest
welcome, and never underestimate the power of making sure your drawings are correct
anonymous
  • anonymous
or where ever it starts at

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