The area enclosed (in square units) by the curve $y=x^4-x^2$,the $x$-axis and the vertical lines passing through the two minimum points of the curve is

Let $f: R \rightarrow R$ be a twice differentiable function such that $f(x + y) = f(x) f(y)$ for all $x, y \in R$. If $f^{\prime}(0) = 4a$ and $f$ satisfies $f^{\prime \prime}(x) - 3a f^{\prime}(x) - f(x) = 0$,$a > 0$,then the area of the region $R = \{(x, y) \mid 0 \leq y \leq f(ax), 0 \leq x \leq 2\}$ is:

The area of the region enclosed by the curve $y=x^3$ and its tangent at the point $(-1,-1)$ is

Area enclosed by the ellipse $9x^2 + 4y^2 = 1$ in the first quadrant is . . . . . . .

The area bounded by the curve $y = \sin x$ between $x = -\pi/2$ and $x = \pi/2$ is . . . . . . .

The area bounded by the parabola $y^2=4ax$ and its latus-rectum $x=a$ is