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comment for which values of $\alpha \in \mathbb R$ is $f$ integrable?
When using polar coordinates, there's a factor $r$ that comes with the Jacobian, so instead of integrating $f(r\cos\theta,r\sin\theta)$ you should be integrating $rf(r\cos\theta,r\sin\theta)$.
Sep
1
answered How to calculate $\lim_{x\to0}\frac{1}{x}\left(\sqrt[3]{\frac{1-\sqrt{1-x}}{\sqrt{1+x}-1}}-1\right)$
Sep
1
revised Consider $F(x,y)=f(x+3y,2x-y)$…
deleted 66 characters in body
Sep
1
comment Consider $F(x,y)=f(x+3y,2x-y)$…
@Willyf Then substitute $x=0, y=0$, what do you get?
Sep
1
revised Consider $F(x,y)=f(x+3y,2x-y)$…
added 1 character in body
Sep
1
answered Consider $F(x,y)=f(x+3y,2x-y)$…
Aug
27
answered Calculus $\int_0^{+\infty}\frac{\sin^2x}x\mathrm dx$
Aug
19
revised $E$ is a certain subspace of $\mathbb{R}[x]$. Is the set $\{x − 2, (x − 2)^2, (x − 2)^3\}$ a basis of $E$?
added 28 characters in body; edited title
Aug
17
reviewed Edit Equation of curve $x=a(\theta- \sin\theta), y=a(1-\cos\theta)$ for varying $\theta$
Aug
17
revised Equation of curve $x=a(\theta- \sin\theta), y=a(1-\cos\theta)$ for varying $\theta$
improved formatting
Aug
17
revised Equation of curve $x=a(\theta- \sin\theta), y=a(1-\cos\theta)$ for varying $\theta$
deleted 24 characters in body; edited title
Aug
17
answered Lie bracket in coordinates
Aug
17
comment Integrate $\int^{\pi }_{0}\frac{x}{2-\tan ^{2}\left( x\right) } dx $
@user257567 What do you get when you use the constraint $x \in (0,\pi)$?
Aug
17
answered For all sets $A$, $B$, and $C$, if $A-B \subseteq A - C$ then $ A \cap C = \varnothing $
Aug
16
comment Integrate $\int^{\pi }_{0}\frac{x}{2-\tan ^{2}\left( x\right) } dx $
@user257567 Find the solutions of the equation $2-\tan^2(x)=0$ for $x\in (0,\pi)$$.
Aug
16
comment Integrate $\int^{\pi }_{0}\frac{x}{2-\tan ^{2}\left( x\right) } dx $
Your function is undefined at $\arctan\sqrt2$ and $\pi-\arctan\sqrt2$ so you can't use this method.
Aug
15
answered Integrate $\int^{\pi }_{0}\frac{x}{2-\tan ^{2}\left( x\right) } dx $
Aug
15
revised Find $\sum_{n=1}^{\infty}a_nx^n$ given $a_0=3, \ 3na_n+3(n-1)a_{n-1}=2a_{n-1}$
added 114 characters in body
Aug
15
answered Convergence of improper integral $\int_{0}^{\frac{\pi}{6}}\dfrac{x}{\sqrt{1-2\sin x}}dx$
Aug
15
answered Find $\sum_{n=1}^{\infty}a_nx^n$ given $a_0=3, \ 3na_n+3(n-1)a_{n-1}=2a_{n-1}$