Walli's Formula: Trig Transformations with Identities and Antiderivatives, Slides of Differential and Integral Calculus

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WALLI’S FORMULA

TRIGONOMETRIC

TRANSFORMATION

WALLI’S FORMULA

OBJECTIVES:

• recall and apply the different

trigonometric identities in transforming

powers of sine and cosine; and

• use Walli’s Formula to shorten the

solution in finding the antiderivative of

powers of sine and cosine

                  _0. 12885 512 21 10 8 6 4 2 2 1 7 5 3 1

1. 3 cos x sin x dx 3 2 2 0 8_                    

2. 8 cos x sin x dx 8 2 3 0 7                 

3. cos 3 x 6 0 8      

 6 2 3 ; u 6 when x when x 0 ; u 0 letu 3 x; du 3 dx           EXAMPLE Evaluate the following integrals.

             

4. sin 2 x 4 0 7       4 2 2 ; u 4 when x when x 0 ; u 0 letu 2 x; du 2 dx          