## Question 40

If the diagram above is the graph of *y* = *x*^{2}, the shaded area is

For you to succeed

If the diagram above is the graph of *y* = *x*^{2}, the shaded area is

A bowl is designed by resolving completely the area enclosed by *y* = *x*^{2} – 1, *y *= 0, *y* = 3 and *x* ≥ 0 around the *y* –axis. What is the volume of this bowl?

The function *f *(*x*) passes through the origin and its first derivative is 3*x* + 2. What is *f*(*x*)?

Find the value of $\int_{0}^{\pi }{\frac{{{\cos }^{2}}\theta -1}{{{\sin }^{2}}\theta }d\theta }$

If the volume of hemisphere is increasing at a steady rate of 18πm^{3}s^{–1} . At what rate is its radius changing when it is 6m

The expression of $a{{x}^{2}}+bx+c$equals 5 at *x* =1. If its derivative is 2*x* + 1, what are the value of *a*, *b*, respectively.

If $y=2x\cos 2x-\sin 2x$, find $\frac{dy}{dx}$when $x=\tfrac{\pi }{4}$

A ship sails a distance of 50km in the direction S50^{o}E and then sails a distance of 50km N40^{o}E. Find the bearing of the ship from its original position.

Find the minimum value of the function $f(\theta )=\frac{2}{3-\cos \theta }\text{ for }0\le \theta \le 2\pi $

$3y=4x-1$and $ky=x+3$are equation of two straight lines. If the two lines are perpendicular to each other, find *k*