Friday, 9 November 2018

calculus - How to evaluate the integral $int_0^{+infty} frac{sin^4{x}}{x^4}dx$?

As we know that $\int_0^{+\infty} \frac{\sin{x}}{x}dx=\pi/2$,but how to evaluate the integral $\int_0^{+\infty} \frac{\sin^4{x}}{x^4}dx$?

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real analysis - How to find $lim_{hrightarrow 0}frac{sin(ha)}{h}$

How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...