Hello everyone, I am having difficulty with this double integral.
I was given the following integral:
\( I =\int ^1_0 dx \int ^{2x}_x 2xy dy \)
I have to reverse the order of integration and so this was my approach:
I first plotted the graph of the above and is attached as 'integrate along y'.
So then I integrated along x so the lower limit is y and y/2. The second image to show what i was thinking is shown as 'figure 2'.
So the integral that I get is:
\( I =\int ^1_0 dy \int ^{y}_{y/2} 2xy dx \)
However, my solution comes to 3/16 whereas the answer should be 3/4.
Thanks fore reading and hopefully one could explain what I am doing wrong!
I was given the following integral:
\( I =\int ^1_0 dx \int ^{2x}_x 2xy dy \)
I have to reverse the order of integration and so this was my approach:
I first plotted the graph of the above and is attached as 'integrate along y'.
So then I integrated along x so the lower limit is y and y/2. The second image to show what i was thinking is shown as 'figure 2'.
So the integral that I get is:
\( I =\int ^1_0 dy \int ^{y}_{y/2} 2xy dx \)
However, my solution comes to 3/16 whereas the answer should be 3/4.
Thanks fore reading and hopefully one could explain what I am doing wrong!
Attachments

11.4 KB Views: 35

14.8 KB Views: 32