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# Part 1: Rules for integrating trigonometric functions sin m x cos n x dx There are three rules governing how we deal with integrals of this form....

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Part 1: Rules for integrating trigonometric functions sin cos m n x xdx There are three rules governing how we deal with integrals of this form. Rule 1.: If the power of the sine is odd and positive, save one sine factor and convert the remaining factors to cosine. Then, expand and integrate. Rule 2: If the power of cosine is odd and positive, save one cosine factor and convert the rest to sine. Then, expand and integrate. Rule 3: If the powers of both the sine and cosine are even and nonnegative, make repeated use of the identities 2 2 1 cos 2 1 cos 2 sin cos 2 2 x x x and x - + = = 4. What relationships between sin and cos are we taking advantage of when we use the rules above? Based on step 2 above what should we set u equal to so that we can make a substitution that allows us to use the general power rule to complete the integration? u = du =

Part 1: Rules for integrating trigonometric functions ∫ sin m x cos n x dx There are three rules governing how we deal with integrals of this form. Rule 1: If the power of the sine is odd and...

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