Various exercises relating to the integration of trigonometric functions.

To fully evaluate the integral from Example trig:reduce_example, it helps to identify the pattern.
Suppose that the power is replaced by an unknown positive constant . Carry out the
calculation again with the unspecified exponent: We conclude Using this formula
several times in a row gives the result

### Sample Quiz Questions

Compute the value of the integral (Hints won’t be revealed until after you choose a response.)

To simplify the calculation, begin with a substitution which replaces with . The
question reduces to computing This integral is compatible with the substitution .

Compute the value of the integral (Hints won’t be revealed until after you choose a response.)

Since the power of secant is odd and the power of tangent is even, try rewriting the
integral in terms of sine and cosine. This gives This integral is compatible with the
substitution .

Compute the value of the integral (Hints won’t be revealed until after you choose a response.)

This integral is compatible with the substitution . By the substitution formula,
this means , and one must also replace by . Furthermore, by virtue of the
special angle formulas and , the problem is reduced to computing the integral