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

Area enclosed by the curves $y = \ln x$,$y = \ln|x|$,$y = |\ln x|$,and $y = |\ln|x||$ is equal to

If $A$ is the area bounded by the curves $y = |\cos x|$ and $y = 5 - \frac{4}{\pi} |x - \pi|$ in $x \in [0, 2\pi]$,then the value of $\left( \frac{A}{2} + 2 \right)$ is

The area of the region bounded by the curves $y=e^x, y=\log x$ and lines $x=1, x=2$ is

The area (in sq. units) of the region described by $A = \{(x, y) : x^2 + y^2 \leq 1 - x\}$ is

The curve $y = ax^2 + bx + c$ passes through the point $(1, 2)$ and its tangent at the origin is the line $y = x$. The area bounded by the curve,the ordinate of the curve at its minima,and the tangent line is