The area (in square units) of the region enclosed between the parabola $y^2=2x$ and the line $y=4x-1$ is:

The area enclosed by the curves $y=\sin x+\cos x$ and $y=|\cos x-\sin x|$ and the lines $x=0, x=\frac{\pi}{2}$ is:

The area bounded by the curves $|x| + |y| \geq 1$ and $x^2 + y^2 \leq 1$ is

The larger of the two areas (in sq. units) into which the circle $x^2+y^2=16a^2$ is divided by the parabola $y^2=6ax$, is

Let for $x \in R$; $f(x) = \frac{x+|x|}{2}$ and $g(x) = \begin{cases} x, & x < 0 \\ x^2, & x \geq 0 \end{cases}$. Then the area bounded by the curve $y = (f \circ g)(x)$ and the lines $y = 0$,$2y - x = 15$ is equal to $...........$.

The area of the figure enclosed by $y = \cos^{-1}(\cos x)$, $x \in [2\pi, 4\pi]$, the $x$-axis, and $y = \tan^{-1} x + \tan^{-1} \frac{1}{x}$ is