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allsmiles
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?
I'm confused with finding the limits for each when you reverse the order anyone got any tips?
drawing out the region of integration is almost always a good idea
|dw:1352232985691:dw|
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?
well what would the area between y^(1/3) and y=8 look like?
it'd be the shaded area under y=8 but above y=x^3?
which we're not looking for right
|dw:1352233420315:dw|you got it :)
so in the area we want we want y bounded above by the function, not the line
it's so hard to see sometimes but got it thanks so much for your help!!
so whenever you want it bounded by the curve you'd take it from 0 to the curve?
welcome, and never underestimate the power of making sure your drawings are correct
or where ever it starts at