Evaluate $\int{\sin 3xdx}$

If $\frac{dy}{dx}=2x-3$and y = 3 when x = 0. Find y in terms of x

Find the area bounded by the curve $y=4-{{x}^{2}}$and $y=2x+1$

Evaluate $\int{2{{(2x-3)}^{\tfrac{2}{3}}}dx}$

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

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.