Is $\int\limits_{0}^{\pi}x\cdot f(\sin x)dx=\pi \cdot \int\limits_{0}^{\pi/2} f(\sin x)dx$?
12604
Evaluate $\int_0^\pi xf(\sin x)dx$
80553
Show that,$\int_0^\pi \left|\frac{\sin nx}{x}\right|\mathrm{d}x \ge \frac{2}{\pi}\left(1+\frac12+\cdots+\frac{1}{n}\right)$
4220
Does $\int_{0}^{\infty}\frac{dx}{1+(x\sin5x)^2}$ converge?
63289
Does $\sum\limits_{x=1}^\infty\sin(x)$ converge?
90313
Integrate $\int_0^\pi{{x\sin x}\over{1+\cos^2x}}dx$.
4693
what is the$ \int \sin (x^2) \, dx$?
83966
Does $ \int_0^{\infty}\frac{\sin x}{x}dx $ have an improper Riemann integral or a Lebesgue integral?
150308
How to prove that $\lim\limits_{n\to\infty}\int\limits _{a}^{b}\sin\left(nt\right)f\left(t\right)dt=0\text { ? }$
129913
Evaluate: $I=\int\limits_{0}^{\frac{\pi}{2}}\ln\frac{(1+\sin x)^{1+\cos x}}{1+\cos x}dx$
91680
Does $\lim_{n\to \infty} \int^{\infty}_{-\infty} f_n(x) dx\, = \int^{\infty}_{-\infty} f(x)\,dx\,$?
67429
Solve $\lim_{x\to0}{\frac{x^2\cdot\sin\frac{1}{x}}{\sin x}}$
139297
Find the sign of $\int_{0}^{2 \pi}\frac{\sin x}{x} dx$
64001
What is the result of $\lim\limits_{x \to 0}(1/x - 1/\sin x)$?
40047
Is $\int_a^b f(x) dx = \int_{f(a)}^{f(b)} f^{-1}(x) dx$?
51837
Show that $\int_{0}^{\pi} xf(\sin(x))\text{d}x = \frac{\pi}{2}\int_{0}^{\pi}f(\sin(x))\text{d}x$
106828
If $0 \lt x \lt \frac{\pi}{2}$, is $\cos(x) \le \frac{\sin(x)}{x} \le \frac{1}{\cos(x)}$?
84413
Why is $\int_{-\infty}^\infty |g(x)|\,dx = \int_0^\infty \mu(\{x : |g(x)| \ge t\})\,dt$ true?