8.3LA_solutions

# 8.3LA_solutions - MthSc 108-Learning Activity Solutions...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MthSc 108-Learning Activity Solutions Section 8.3: Trigonometric Substitutions 1. 2 2 9 x dx x- âˆ« Solution: Use the method of trigonometric substitution with the substitution 3sin x Î¸ = for - Ï€ 2 â‰¤ Î¸ â‰¤ Ï€ 2 and 3cos dx d Î¸ Î¸ = . Then 2 2 2 9 9 9sin 9cos 3cos x Î¸ Î¸ Î¸- =- = = and ( ) 2 2 2 2 2 9 3cos 3cos cot csc 1 cot 9sin x dx d d d C x Î¸ Î¸ Î¸ Î¸ Î¸ Î¸ Î¸ Î¸ Î¸ Î¸- = = =- = -- + âˆ« âˆ« âˆ« âˆ« Now the solution needs to be rewritten in terms of the variable x. We have that sin 3 x Î¸ = and using a right triangle with angle Î¸ the opposite side is x and the hypotenuse is 3. So the adjacent side is 2 9 x- . 2 2 2 9 9 cot arcsin 3 x x x dx C C x x Î¸ Î¸-- = -- + = -- + âˆ« 2. Find the volume of the solid generated by revolving about the x-axis, the region in the first quadrant enclosed by the coordinate axes, the curve 2 2 1 y x = + , and the line 1 x = ....
View Full Document

## This note was uploaded on 01/30/2011 for the course MTHSC 108 taught by Professor Any during the Spring '08 term at Clemson.

### Page1 / 3

8.3LA_solutions - MthSc 108-Learning Activity Solutions...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online