chap7sec3

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

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Unformatted text preview: 7.3 Trigonometric Substitution 2 2 a x dx- ∫ 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. Problem 2 3 2 2 2 2 2 2 3 2 3 5 3 2 5 2 2 5 9 sin 3sin 9 9sin 9(1 sin ) 3 cos 3 cos 3cos ( ) 3sin 3cos 9 (3sin ) (3cos )(3cos ) 3 sin cos 3 sin cos sin (Use sub. from 7.2) cos sin 3 x x dx x a x dx d x x dx d d d u du d π π θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ- = =- =- = = =- ≤ ≤ = ⇒ =- = = = = = - = - ∫ ∫ ∫ ∫ ∫ 2 2 5 2 2 5 2 4 5...
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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 2 2 a x dx ...

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