Let $$f:IR \to IR$$ be defined as $$f\left( x \right) = \left| x \right| + \left| {{x^2} - 1} \right|.$$ The total number of points at which $$f$$ attains either a local maximum or a local minimum is

The integral $\int \frac{\sec ^2 x}{(\sec x+\tan x)^{9 / 2}} d x$ equals (for some arbitrary constant $$K$$)

Let $$S$$ be the area of the region enclosed by $$y = {e^{ - {x^2}}}$$, $$y=0$$, $$x=0$$, and $$x=1$$; then

If $$y(x)$$ satisfies the differential equation $$y' - y\,tan\,x = 2x\,secx$$ and $$y(0)=0,$$ then