Nov 10, 2024 · Problem: Find the surface integral $I=\\iint_S2x^2ydydz-y^2dzdx+4xz^2dxdy$, where $S$ is curved surface of the cylinder $y^2+z^2=9$ bounded by the planes $x=0,\\,x=2 ...

Possible Duplicate: Explain $\\iint \\mathrm dx\\mathrm dy = \\iint r \\mathrm d\\alpha\\mathrm dr$ I'm reading the proof of Gaussian integration. When we change to polar coordinates, why do …

Aug 15, 2013 · How would you go about changing the order of integration in a function say ; $$\\int_0^8\\int_\\sqrt[3]{y}^2 f(x,y)~dx~dy$$

Update: Two things have happened: Rankeya has given a valid answer to the written question, but I realize now I was too vague. Secondly, I looked up the correct exercise in Jacobson and …

Apr 8, 2018 · I understand the meaning of $\frac {dy} {dx}$ and $\int f (x)dx$, but outside of that what do $dy, du, dx$ etc.. mean? When I took calc I, derivatives and integrals ...

Aug 31, 2020 · Use a Kronecker product to flatten the matrix to a vector, i.e. $\,W\to w.\,$ Then the equation becomes $ (x\otimes I)^Tw +b$ whose gradient is $ (x\otimes I)$.

Oct 7, 2015 · its actually $\dot x$ or $\frac {dx} {dt}$, the term inside of the integral.

May 2, 2015 · Okay this may sound stupid but I need a little help... What do $\\Large \\frac{d}{dx}$ and $\\Large \\frac{dy}{dx}$ mean? I need a thorough explanation. Thanks.

Apr 2, 2017 · Expanding out $ (x-y)^2$, we get $$ x^2+ (x-y)^2+y^2=2 (x^2-xy+y^2)$$ Then complete the square: $$ x^2-xy+y^2=\Big (x-\frac {y} {2}\Big)^2+\frac {3y^2} {4} $$ so that ...

Jan 12, 2016 · As noted in the comments, your derivation contains a mistake. To answer the question, this function can not be integrated in terms of elementary functions. So there is no …