I actually understood everything except two things, the explanation of why is the jacobian needed, and when changing limits of the integral (the upper and bottoms values) in any of the triangles didnt understand why the second integral had u and -u as bottom and upper limits
Hi, it seems that your doubts are related to a lack of familiarity with changes of variables in multiple integrals. The points you highlighted (i.e. the Jacobian, the limits of integration) can be understood without much of an effort provided you understand how to do a change of variables in a generic double integral. I hope this might give you some hints on how to improve.
@@math.physics after thinking for a while I think the upper and bottom limits correspond to doing an integral of the triangle first, from the left to the mid of triangle and then because of the change of the slope after the mid part of triangle you integrate again from mid to right part. In the video he did it in just one integral and i got confused. Still, i dont understand the Jacobian (I supose if you change the variables then differencials also do) so you are right, I still need to learn quite a lot
Anyway thank you for explaining this way to calculate this integral bacuse i havent found any video about it. Now I can demonstrate myself the basel problem, thank you👍
@@markellacabe7171you are welcome. Over the next weeks, if I find some time, I will do the derivation of the Basel problem in a more intuitive way, without calculating any double integrals. I will post the video on this channel.
I like this proof. A smart little trick at the beginning and just raw dogging till the end. Euler would be proud.
how do you generalise to evaluate zeta(4) with integrate_0^1 1/(1-xyzw) dx dy dz dw --> Pi^4/90?
I think I've run into this approach in Apostol.
such a nice solution
I actually understood everything except two things, the explanation of why is the jacobian needed, and when changing limits of the integral (the upper and bottoms values) in any of the triangles didnt understand why the second integral had u and -u as bottom and upper limits
Hi, it seems that your doubts are related to a lack of familiarity with changes of variables in multiple integrals.
The points you highlighted (i.e. the Jacobian, the limits of integration) can be understood without much of an effort provided you understand how to do a change of variables in a generic double integral.
I hope this might give you some hints on how to improve.
@@math.physics after thinking for a while I think the upper and bottom limits correspond to doing an integral of the triangle first, from the left to the mid of triangle and then because of the change of the slope after the mid part of triangle you integrate again from mid to right part. In the video he did it in just one integral and i got confused. Still, i dont understand the Jacobian (I supose if you change the variables then differencials also do) so you are right, I still need to learn quite a lot
Anyway thank you for explaining this way to calculate this integral bacuse i havent found any video about it. Now I can demonstrate myself the basel problem, thank you👍
@@markellacabe7171you are welcome. Over the next weeks, if I find some time, I will do the derivation of the Basel problem in a more intuitive way, without calculating any double integrals. I will post the video on this channel.
@@math.physics I’ll watch it👍
💕 p͎r͎o͎m͎o͎s͎m͎