The average ordinate of $y = \sin x$ over $[0, \pi]$ is

If $[.]$ represents the greatest integer function,then the value of $\int_{0}^{\sqrt{\pi / 2}}\left(\left[ x ^{2}\right]+[-\cos x ]\right) d x$ is.............

$\int_0^\pi \frac{1}{1+\sin x} dx$ is equal to

Let $g(x) = \int_0^x f(t) \, dt$ where $\frac{1}{2} \le f(t) \le 1$ for $t \in [0, 1]$ and $0 \le f(t) \le \frac{1}{2}$ for $t \in (1, 2]$. Then which of the following is true for $g(2)$?

$\int_{\frac{\pi}{3}}^{\frac{\pi}{2}} \frac{\sqrt{1+\cos x}}{(1-\cos x)^{\frac{5}{2}}} d x=$

$\int_1^4 \left(x + \sqrt{x} + \frac{1}{x}\right) dx - \int_1^{2 \log 2} dx = $