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bio website qoqosz.net
location Poland
age 25
visits member for 2 years, 7 months
seen Nov 26 at 21:25

I'm just a physics student.


Jun
10
comment Evaluate $\lim_{x \to \infty} \frac{1}{x} \int_x^{4x} \cos\left(\frac{1}{t}\right) \mbox {d}t$
$f'(x) = \cos \left( \frac{1}{4x} \right) (4x)' - \cos \left( \frac{1}{x} \right) (x)'$ check this article on wikipedia - en.wikipedia.org/wiki/Fundamental_theorem_of_calculus
Jun
10
comment Evaluate $A_r=\int_{{0}}^{\frac{\pi}{2}} \sin^{r}x \ \ dx$
First write: $A_r = \int_0^{\pi /2} (1 - \cos^2 x) \cdot \sin^{r-2} x \, dx = A_{r-2} - \int_0^{\pi/2} \cos^2 x \, \sin^{r-2} x \, dx$ and for integration by parts take: $u = \cos x, \; v' = \cos x \, \sin^{r-2} x$.
Jun
10
revised Equivalent of $ I_{n}=\int_0^1 \frac{x^n \ln x}{x-1}\mathrm dx, n\rightarrow \infty$
deleted 3 characters in body
Jun
10
comment Equivalent of $ I_{n}=\int_0^1 \frac{x^n \ln x}{x-1}\mathrm dx, n\rightarrow \infty$
@TenaliRaman you're right, I haven't noticed this divergence before. Thanks!
Jun
10
comment Equivalent of $ I_{n}=\int_0^1 \frac{x^n \ln x}{x-1}\mathrm dx, n\rightarrow \infty$
@RagibZaman sure, but here $I_n$ behaves fine enough.
Jun
10
answered Equivalent of $ I_{n}=\int_0^1 \frac{x^n \ln x}{x-1}\mathrm dx, n\rightarrow \infty$
Jun
10
revised plotting the following set of points in the XY plane
Use LaTeX to write equations
Jun
10
suggested approved edit on plotting the following set of points in the XY plane
Jun
9
comment Is there a simple way of arriving at this solution?
@Thomas yes, but is such generalization needed?
Jun
9
answered Is there a simple way of arriving at this solution?
Jun
9
revised expectation of product of independent random variable
Use LaTeX to write equations
Jun
9
suggested approved edit on expectation of product of independent random variable
Jun
9
awarded  Organizer
Jun
9
awarded  Editor
Jun
9
comment Norm of integral operator in $L_2$
@Norbert :D it's also quite common exercise ;)
Jun
9
revised looking for a norm inequality
Use LaTeX to write equations
Jun
9
suggested approved edit on looking for a norm inequality
Jun
9
answered Integral of product of exponential function and two complementary error functions (erfc)
Jun
9
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Jun
9
awarded  Nice Answer