Evaluate the integral.

a$.{\displaystyle \underset{\frac{1}{4}}{\overset{\frac{\sqrt[\phantom{2}]{3}}{4}}{}}}\sqrt[\phantom{2}]{1-4x^2}dx$

b$.{\displaystyle \underset{0}{\overset{1}{}}}\sqrt[\phantom{2}]{x-x^2}dx$

Find the area of the region bounded by the hyperbola $9x^2-4y^2=36$ and the line $x=3.$

Find the volume of the solid obtained by rotating about the $x-$axis the region enclosed by the curves

$y=\frac{9}{x^2+9},y=0,x=0,$ and $x=3$