If the diagram above is the graph of y = x², the shaded area is

A bowl is designed by resolving completely the area enclosed by y = x² – 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 3x + 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 18πm³s^–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 2x + 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^oE and then sails a distance of 50km N40^oE. 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