**(a) Formulae for volume**of the cylinder, cone, sphere, and various parabaloids using two methods; the slab (disk) method and the shell method.

**(b) Formulae for surface area**of the cone and sphere using similar methods to those mentioned above.

**(c) Formulae for area**of the circle and ellipse.

**(d) Formula for arc length**of a circle given its central angle. For this, we will reference the Mean Value Theorem and our knowledge of differentiaion.

Before proceeding any further, however, a "new" method of integration must be introduced, that being Integration by Trigonometric Substitution; this was eluded to in the previous set of notes. The example illustrated on pages 20 & 21 in my notes on Integration by Partial Fractions revealed that the antiderivative of the expression "[3/(x^2+1)]" was "[3arctan(x)]". This method and the reasoning behind it will be explained in my next set of notes; we will also be made aware of why the "Natural Logarithm Method"

**WILL NOT**work for this expression. My notes on Integration by Trigonometric Substitution can be found in the link directly below.

Integration by Trigonometric Substitution - Samuelson

Visit the links below for additional information on this method of integration. The first one takes you to a lecture given by a guest instructor at MIT.

Trigonometric Substitution & Polar Coordinates

Integration by Trigonometric Substitution (1)

Integration by Trigonometric Substitution (2)

Integrating Algebraic Functions