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## Search found 307 matches

Mon Nov 27, 2017 10:42 am
Forum: Real Analysis
Topic: Sequence and limit of integral
Replies: 1
Views: 1711

Replies: 0
Views: 1382

### $\int_{0}^{\pi}\arcsin(1-\sin{t})\,dt$

Does this $$\displaystyle\int_{0}^{\pi}\arcsin(1-\sin{t})\,dt$$
can be (accurately) evaluated?
Sun Sep 24, 2017 6:37 pm
Forum: Multivariate Calculus
Topic: Volume and area of a solid
Replies: 1
Views: 1440

### Volume and area of a solid

Let $a,b,c,d$ positive real numbers such that $a<b$, $d^2=\dfrac{b-a}{2c}$ and the closed disk $D=\big\{(x,y)\in{\mathbb{R}}^2\;\big|\;(x-x_0)^2+(y-y_0)^2\leqslant d^2\big\}\,.$ Find the volume and the surfase area of the solid \[V=\Big\{(x,y,z)\in{\mathbb{R}}^3\;\big|\;(x,y)\in{D}\,,\; a+c(x-x_0)...
Tue Sep 19, 2017 7:48 pm
Forum: Multivariate Calculus
Topic: A tough limit
Replies: 1
Views: 1546

### Re: A tough limit

The function $f(x,y)=x^y\,,\; (x,y)\in{\mathbb{R}}^2\,,$ is at least twice continuously differentiable in a open disk with centre $(1,1)$ and its 2nd degree Taylor polynomial is \begin{align*} P_{2,f,(1,1)}(x,y)&=f(1,1)+({\rm{grad}}\,{f})(1,1)\cdot(x-1,y-1)+\frac{1}{2}\,(x-1,y-1)\,H_f(1,1)\,(x-1,y-1...