- #1

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- Homework Statement
- Calculate the double integral of y^2 - 4x over the following region -y^2 < x < y^2 , 0 < y < 1

- Relevant Equations
- I did the integral by dividing the region into strips parallel to the x-axis and got the answer 2/5 which i know is correct but i am trying to reverse the order of integration but i can't get the same answer

Performing the x-integration first the limit are x=y

But i am getting confused when trying to reverse the order of integration. My attempt is that i have to divide the region in 2 equal halfs and then double my answer at the end. I used y limits from √x to 1 and x limits from 0 to 1 but i am ending up with the answer zero ! Where am i going wrong with my limits here ?

Thanks

^{2}and x= -y^{2}and then the y limits are 0 to 1. This gives the final answer 2/5But i am getting confused when trying to reverse the order of integration. My attempt is that i have to divide the region in 2 equal halfs and then double my answer at the end. I used y limits from √x to 1 and x limits from 0 to 1 but i am ending up with the answer zero ! Where am i going wrong with my limits here ?

Thanks