8.3LA_solutions

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

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Unformatted text preview: MthSc 108-Learning Activity Solutions Section 8.3: Trigonometric Substitutions 1. 2 2 9 x dx x- Solution: Use the method of trigonometric substitution with the substitution 3sin x = for - 2 2 and 3cos dx d = . Then 2 2 2 9 9 9sin 9cos 3cos x - =- = = and ( ) 2 2 2 2 2 9 3cos 3cos cot csc 1 cot 9sin x dx d d d C x - = = =- = -- + Now the solution needs to be rewritten in terms of the variable x. We have that sin 3 x = and using a right triangle with angle 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 -- = -- + = -- + 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 = ....
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8.3LA_solutions - MthSc 108-Learning Activity Solutions...

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