The area of the region enclosed by the curves $y=e^x, y=\left|e^x-1\right|$ and $y$-axis is:

The area bounded by the $y-$ axis, $y=\cos x$ and $y=\sin x$ when $0 \leq x \leq \frac{\pi}{2}$ is

Let $f :[-3,1] \rightarrow R$ be given as

$f(x)=\left\{\begin{array}{ll} \min \left\{(x+6), x^{2}\right\}, & -3 \leq x \leq 0 \\ \max \left\{\sqrt{x}, x^{2}\right\}, & 0 \leq x \leq 1 \end{array}\right.$

If the area bounded by $y = f ( x )$ and $x$ -axis is $A,$ then the value of $6 A$ is equal to ....... .

The area of the region bounded by $y-x=2$ and $x^{2}=y$ is equal to :

Area bounded by the curve $y = \min \{\sin^2x, \cos^2x \}$ and $x-$ axis between the ordinates $x = 0$ and $x = \frac{{5\pi }}{4}$ is