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

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?

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

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

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

Evaluate $\int_{0}^{\tfrac{\pi }{2}}{\sin 2xdx}$

Evaluate $\int_{-4}^{0}{(1-2x)dx}$

Integrate $\frac{{{x}^{2}}-\sqrt{x}}{x}$ with respect x

Evaluate $\int_{1}^{2}{(6{{x}^{2}}-2x)dx}$

Evaluate  $\int_{0}^{2}{({{x}^{3}}+{{x}^{2}})dx}$

Evaluate $\int\limits_{0}^{1}{(3-2x)dx}$

Evaluate $\int_{1}^{2}{({{x}^{2}}-4x)dx}$

$\begin{align}  & \text{Integrate }\left( \frac{1+x}{{{x}^{3}}} \right)dx \\ & \text{(A) }-\frac{1}{2{{x}^{2}}}-\frac{1}{x}+k\text{  (B) }-\frac{{{x}^{2}}}{2}-\frac{1}{x}+k\text{   (C) }{{x}^{2}}-\frac{1}{x}+k\text{   (D)  }2{{x}^{2}}-\frac{1}{x}+k \\\end{align}$

Evaluate $\int{\sin 2xdx}$

Evaluate $\int{\sin 4xdx}$

Integrate $\frac{2{{x}^{3}}+2x}{x}$ with respect to x

Evaluate $\int\limits_{0}^{\tfrac{\pi }{2}}{\sin xdx}$

The gradient of a curve is 2x + 7 and the curve passes through point (2,0). Find the equation of the curve

Evaluate $\int{\sin 3xdx}$