Show that $\frac{2}{\pi}x<\sin x<x$ for $0<x<\frac{\pi}{2}$
11387
Mean Value Theorem: $\frac{2}{\pi}<\frac{\sin x}{x}<1$
46310
Showing that $ \int_{0}^{1} \frac{x-1}{\ln(x)} \mathrm dx=\ln2 $
158279
$\int_0^{\pi/2}\ln(\sin(x))$?
60559
How prove this $x^3<\sin^2{x}\tan{x},x\in\left(0,\dfrac{\pi}{2}\right)$
103598
Showing that $\int_0^1 \log(\sin \pi x)dx=-\log2$
72278
What is the value of $\frac{\sin x}x$ at $x=0$?
103513
Show that $\lim_{n\to \infty}\int_{-\pi}^{\pi}f(x)g(nx)\,dx=\frac{1}{2\pi}\int_{-\pi}^{\pi}f(x)\,dx\int_{-\pi}^{\pi}g(x)\,dx$
95266
Show $|t|\leq \pi \Rightarrow |e^{it}-1|\geq 2|t|/ \pi$
114734
Prove that $\frac{1}{2\pi i}\int_\mathcal{C} |1+z+z^2+\cdots+z^{2n}|^2~dz =2n$ where $\mathcal{C}$ is the unit circle
16775
Showing that $\int_{0}^{\infty} \frac{dx}{1 + x^2} = 2 \int_0^1 \frac{dx}{1 + x^2}$
24469
Prove $ 2<(1+\frac{1}{n})^{n}$
88097
Fourier series for $f(x)=(\pi -x)/2$
144811
Calculate $\int_0^{2\pi} \frac{1}{2+\sin(x)} \ dx$
118701
Evaluate $\int_{0}^{\frac{\pi }{2}}\frac{x dx}{\sin x +\cos x}$
35529
Prove that $\sin x+2x\ge\frac{3x(x+1)}{\pi}$ for all $x\in [0,\frac{\pi}{2}]$
62173
How do I show that $\int_0^\infty \frac{\sin(ax) \sin(bx)}{x^{2}} \, \mathrm dx = \pi \min(a,b)/2$
22709
Show that $\lim_{x\to \frac{\pi}{2}} \frac{1}{\big(x-\frac{\pi}{2}\big)}+{\tan(x)}=0$.