chap7sec3

chap7sec3 - 7.3 Trigonometric Substitution a 2 x 2 dx...

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7.3 Trigonometric Substitution 22 ax d x arises when finding the area of a circle or an ellipse (a>0), This can’t be done with regular substitution so we will look at a method of substitution called trigonometric substitution . There are some problems that can be done with either regular substitution or trig substitution. These are of a specific form - not just any integral with a square root. We will refer to the table on page 484 when working these problems. The examples we will do in class are #2,6,and 16.
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Problem 2 32 22 2 3 53 2 52 2 5 9 sin 3sin 9 9sin 9(1 sin ) 3 cos 3 cos 3cos ( ) 9 (3sin ) (3cos )(3cos ) 3s i n c o s 3 sin cos sin (Use sub. from 7.2) cos sin 3 xx d x x a xd x d x x dx d d d u du d ππ θθ θ −= = == =⇒ = = = =− ∫∫ = = 5 2 2 524 542 55 3 5 5 3 11 1 1 5 3 2 3 (1 cos )cos sin 3 ) 3( ) ) 33 c o s c o s Now we must find a representation for cos in terms of . Using sin we get cos 1 sin 1 du u d u uu d u d u uuC C x =  + = − +  = 2 9 5 99 93 19 3 (You can leave it here.)
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This note was uploaded on 01/20/2012 for the course MATH 2057 taught by Professor Estrada during the Fall '08 term at LSU.

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chap7sec3 - 7.3 Trigonometric Substitution a 2 x 2 dx...

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