Show that $\int_0^\pi f(\sin\theta) \, d\theta = 2\int_0^{\pi/2}f(\sin\theta) \, d\theta$
76408
Show that $\int_0^\pi f(\sin x)\,\mathrm{d}x = 2\int_0^{\pi/2}f(\sin x) \, \mathrm{d}x$
36697
Proving that $\int_{-b}^{-a}f(-x)dx=\int_{a}^{b}f(x)dx$
103598
Showing that $\int_0^1 \log(\sin \pi x)dx=-\log2$
135447
Compute the integral $\int_0^{\frac\pi2}\frac{\mathrm d \theta}{\sqrt{\sin \theta}}$
62173
How do I show that $\int_0^\infty \frac{\sin(ax) \sin(bx)}{x^{2}} \, \mathrm dx = \pi \min(a,b)/2$
101030
Integration $I_n=\int _0^{\pi }\sin^{2n}\theta d\theta $
126736
Show that $\lim_{\epsilon\to0^{+}}\frac{1}{2\pi i}\int_{\gamma_\epsilon}\frac{f(z)}{z-a} \, dz=f(a)$
154264
$f \in C[-1,1]$, Prove ${\lim_{h \to 0^+}}{\int_{-1}^1 \frac{h}{h^2+x^2}f(x)\,dx} = \pi f(0)$
69000
Looking for closed-forms of $\int_0^{\pi/4}\ln^2(\sin x)\,dx$ and $\int_0^{\pi/4}\ln^2(\cos x)\,dx$
129443
$f(\theta) = \cos \theta - \sqrt{3}\sin \theta$ in the form $r\sin(\theta-\alpha)$
156881
How prove this inequality $I=\int_{0}^{\sqrt{2\pi}}\sin{x^2}dx>0$
85814
Quotient of two integrals $\frac{\int_0^\pi x^3\ln(\sin x)\,dx}{\int_0^\pi x^2\ln(\sqrt{2}(\sin x))\,dx}$
61162
Show that $\left(\int_0^1 f(x)\,dx\right)^2\leq2\int_0^1x\, f(x)^2\,dx $
70715
How do I prove $\int_0^\pi\frac{(\sin nx)^2}{(\sin x)^2}dx = n\pi$?
94869
Show that $ \int_{k}^{2} \frac{1}{f(y)} =1$
139057
Showing that $\frac{1}{2\pi}\int^{2\pi}_{0}(2\cos\theta)^{2n}d\theta=\frac{(2n)!}{n!n!}$
86857
Integrate $\int_{0}^{2\pi}\log|1-e^{i\theta}| d\theta$