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 ...

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.

The statement is imprecise: eigenvectors corresponding to distinct eigenvalues of a symmetric matrix must be orthogonal to each other. Eigenvectors corresponding to the same eigenvalue need not be …

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 we get an "

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 ...

I've just started reading through Calculus Made Easy by Silvanus Thompson and am trying to solidify the concept of differentials in my mind before progressing too far through the text. In Chapter 1

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

@Garmen: Please take a look at my comments under the answer you accepted. That answer is quite misleading; one of the limits is wrong, and the concept "infinitesimally small" is being used informally …

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 "simple" answer to …