Evaluate \(\int _{ b }^{ \infty }{ \frac { 1 }{ { a }^{ 2 }+{ x }^{ 2 } } dx,a>0,b\in R } \)

Evaluate the following
\(\int _{ 0 }^{ 1 }{ { x }^{ 2 }{ (1-x) }^{ 3 }dx } \)

Find the area of the region bounded by the curve y = sin x and the ordinate x=0 \(x=\frac { \pi }{ 3 } \) 

Find the area enclosed between the parabola y²=4ax and the line x=a, x=9a.

Find the area bounded by the curve y = cosax in one arc of the curve.