For basic questions about limits, derivatives, integrals, and applications, mainly of one-variable functions.

learn more… | top users | synonyms

5
votes
1answer
96 views
+100

Modeling Rain on a Windshield for various Speeds using Calculus

A question was recently posed to Click & Clack Talk Cars (http://www.greatfallstribune.com/story/life/2014/08/07/click-clack-rainy-day-raises-physics-question/13750681/). The topic is rain hitting ...
0
votes
1answer
45 views
+50

Converting a slope field into a vector field

I have homework on slope fields where I have to graph a bunch and find the equillibrium solution, but instead of taking such a long time to graph them, I decided to use WolframAlpha. Sadly, there is ...
28
votes
5answers
601 views
+200

How to find ${\large\int}_0^1\frac{\ln^3(1+x)\ln x}x\mathrm dx$

Please help me to find a closed form for this integral: $$I=\int_0^1\frac{\ln^3(1+x)\ln x}x\mathrm dx\tag1$$ I suspect it might exist because there are similar integrals having closed forms: ...
20
votes
2answers
376 views
+500

Integral ${\large\int}_0^\infty\frac{\ln x}{1+x}\sqrt{\frac{x+\sqrt{1+x^2}}{1+x^2}}\ \mathrm dx$

Please help me to evaluate this integral: $$ I={\large\int}_{0}^{\infty}{\ln\left(x\right) \over 1 + x}\, \,\sqrt{\,x + \sqrt{\,1 + x^{2}\,}\, \over 1 + x^{2}\,}\,\,{\rm d}x.\tag1 $$ Mathematica could ...
2
votes
1answer
45 views
+50

Without using Stokes theorem, compute surface and line integrals

Let S be the surface in $R^3$ given by the part of the sphere $x^2+y^2+z^2=2$ that lies above the plane $z=1$. Let v(x,y,z) be the vector field given by $v(x,y,z)=(z,x,z)$. a) Without using Stokes' ...
4
votes
0answers
48 views
+100

'Deriving' the Laplace Transform from the $z$ Transform: Missing a $\Delta t$

Textbooks normally give the following 'derivation' (or justification, if you prefer) of the z-Transform from the Laplace Transform. Let $x(t)$ be a signal defined on $t\geq 0$, and write a discretized ...