Curvature-radius of curvature in Cartesian and polar forms-evolutes and envelopes pedal equations

Integration of f’(x)/f(x), f’(x)√f(x), [(px+q)/√(ax2+bx+c)],[√(x-a)/(b-x)], [√(x-a)(b-x)],1/[√(x-a)(b-x)], [1/(acosx+bsinx+c)], [1/(acos2x+bsin2x+c)] and Integration by parts.

Reduction formulae-problems-evaluation of double and triple integrals-applications to calculations of areas and volumes-areas in polar coordinates.

Change of order of integration in double integral-Jacobions- change of variables in double and triple integrals.

Beta and Gamma Integrals-their properties, relation between them-evaluation of multiple integrals using Beta and Gamma functions