Integration - Assignment Example

Partial fractions is a simple integration where the denominator has got irreducible quadratic factors of which are not repeated. The method is based on a simple concept by adding the denominators to get a common denominator. In order to generate a torus, we do revolve the area within a circle. X^2 + (y-b) ^2 = a^2 about the x-axis. We can solve this as y = b±. This divides the upper half circle and lower half circle. The area can now be divided into vertical rectangles and revolve each to generate a disc with a hole.

In any case the outer radius is be R and the inner radius be r, then the disc with hole volume becomes () dx. This is due to the fact that the cross sectional area is the area of the two circles. R is the y-value of the upper half circle: R = b + and r is the y value of the smaller lower half