Problem Set 2

Problem 1

integrate:

Mathcad solution

rearranging:

AND REMEMBERING

Integrating by parts where:

*** see below

=

So ...

***show:

and remembering:

we can do this by differentiating sin(x)/cos(x) to obtain the integrand thus:

where

=

Problem 2

Mathcad solution

lets simplify the integrand first:

using integration rules we have for these two trig functions yields:

So ...

Problem 3

Mathcad solution:

Using the rule:

where:

equation [3A]

but using the rule:

where:

substituting into equation [3A]

yields:

Lets comparing the Mathcad solution with the hand solution over the domain:

The functions overlay and are identical.

Just for kicks, lets show the two functions are identical

given

replacing sin(2x)

expanding

multiply through by 30

factoring

dividing both sides by sin(x)cos(x)

simplify

--------- some identities --------