Tagged Questions

127 views

Areas and Volumes using integrals [closed]

I am practising for an engineering calculus exam from past year papers. My main problem topic is Integration. My exam is in one day and I need help on how to find areas and volumes of graphs using ...
59 views

Separation of variables (ODEs)

Here is the question I am currently stuck on: Here is what I have done so far: My apologies as I understand this post seems fairly lengthy. However I cannot seem to get the final answer ...
379 views

Where is Greens theorem used?

Where is Greens theorem used? I think it's weird going from a vector field to calculating a volume on a scalar field, where do we use this kind of calculation?
208 views

Problem with calculating a winding number

I have a problem with calculating the winding number $n\left ( \gamma ,\frac{1}{3} \right )$ of the curve $\gamma :\left [ 0,2\pi \right ]\rightarrow \mathbb{C}, t \mapsto \sin(2t)+i\sin(3t)$. ...
305 views

Circumference of a superellipse?

Could someone help me formulate the circumference of a superellipse? $$\frac{x^n}{a^n} + \frac{y^n}{b^n} = 1$$ If it makes things easier, I'm considering only the cases $n>2$, and ...
156 views

Symbolic integration of vector norm

I'd like to symbolically integrate the expression $\int_0^1{\|r'\left(t\right)\|_2\,dt}$ where $r$ is a function $\mathbb{R} \rightarrow \mathbb{R}^2$ (so the expression is the arc length of the curve ...
547 views

Find area of a simple, smooth, closed curve lying in a plane

I was given this question in class and I assume it is a spin off of Green's theorem for finding the area of a closed curve $\lambda$ in 2D but expanded to 3D I believe. Anyways I am pretty confused ...
660 views

How to calculate the area between 2 polar curves: $r=\frac{4}{2}-\sin\theta$ and $r=3\sin\theta$?

How to calculate the area between 2 polar curves: $r=2-\sin\theta$ and $r=3\sin\theta$? I know that one curve is a limaçon and the other is a circle. I have them drawn out as well, my only question ...
184 views

Length of a plane curve in polar coordinate

Consider the plane curve $\gamma$ in polar coordinates: $$r=r_0+e^{\lambda\theta}, \quad \theta_1 \le \theta \le \theta_2,$$ where $r_0,\lambda,\theta_1>0$. Is it possible to compute explicitly ...
I'm watching this video, where D. Knuth explains the connection of $\pi$ and factorials, and other matters (it is very interesting). Almost at the end of the talk he says the area of the superellipse ...
How do I analytically calculate using integration the area under the following curve? $$x^2+ xy + y^2= 1$$ Its some ellipse and I see it might help that it's symmetric in exchange of x and y, so ...