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Various exercises relating to the integration of trigonometric functions.

Compute the indefinite integrals below. Since there are many possible answers (which differ by constant values), use the given instructions if needed to choose which possible answer to use.
(Add a constant to your answer if needed so that it equals $0$ at $x = 0$.)
(Add a constant to your answer if needed so that it equals $-2/15$ at $x = 0$.)
You can either use an integration by parts technique or you can use a trigonometric identity to simplfy the expression $\cos Ax \sin Bx$ (for constants $A$ and $B$) as a sum of simpler things.
(Your answer should not include any constant terms and should equal $0$ at $x = 0$.)
Use power reduction formulas.
To fully evaluate the integral from Example trig:reduce_example, it helps to identify the pattern. Suppose that the power $7$ is replaced by an unknown positive constant $n > 2$. 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.)

$\displaystyle \frac {1}{5}$ $\displaystyle \frac {1}{3}$ $\displaystyle \frac {1}{2}$ $\displaystyle 1$ $\displaystyle 2$ $\displaystyle 3$

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

$\displaystyle \frac {17}{5}$ $\displaystyle \frac {19}{5}$ $\displaystyle \frac {23}{5}$ $\displaystyle \frac {29}{5}$ $\displaystyle \frac {31}{5}$ $\displaystyle \frac {37}{5}$

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

$\displaystyle \frac {1}{5}$ $\displaystyle \frac {1}{3}$ $\displaystyle \frac {1}{2}$ $\displaystyle 1$ $\displaystyle 2$ $\displaystyle 3$

### Sample Exam Questions

Compute the integral below.

$\displaystyle \frac {4}{9}$ $\displaystyle \frac {7}{24}$ $\displaystyle \frac {5}{14}$ $\displaystyle \frac {9}{28}$ $\displaystyle \frac {6}{35}$ $\displaystyle \frac {1}{7}$