The area of the region lying in the first quadrant and bounded by the curve $y = 4x^2$, the Y-axis, and the lines $y = 2$, $y = 4$ is...

The area bounded by the curves $y = |x| - 1$ and $y = -|x| + 1$ is

If $y = f(x)$ is a monotonically increasing function such that $\left(\dfrac{dy}{dx}\right)^2 = 6 - \dfrac{dy}{dx}$ and $y(0) = 5$, then $y(3) = \cdots$

If $\tan x$ is an integrating factor of the differential equation $\dfrac{dy}{dx} + Py = Q$, then $P$ can be