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 Jun10 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 Jun10 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: $u = \cos x, \; v' = \cos x \, \sin^{r-2} x$. Jun10 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 Jun10 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! Jun10 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. Jun10 answered Equivalent of $I_{n}=\int_0^1 \frac{x^n \ln x}{x-1}\mathrm dx, n\rightarrow \infty$ Jun10 revised plotting the following set of points in the XY plane Use LaTeX to write equations Jun10 suggested approved edit on plotting the following set of points in the XY plane Jun9 comment Is there a simple way of arriving at this solution? @Thomas yes, but is such generalization needed? Jun9 answered Is there a simple way of arriving at this solution? Jun9 revised expectation of product of independent random variable Use LaTeX to write equations Jun9 suggested approved edit on expectation of product of independent random variable Jun9 awarded Organizer Jun9 awarded Editor Jun9 comment Norm of integral operator in $L_2$ @Norbert :D it's also quite common exercise ;) Jun9 revised looking for a norm inequality Use LaTeX to write equations Jun9 suggested approved edit on looking for a norm inequality Jun9 answered Integral of product of exponential function and two complementary error functions (erfc) Jun9 awarded Supporter Jun9 awarded Nice Answer