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MTH132-Quiz7-Solutions (1)

# MTH132-Quiz7-Solutions (1) - Page 1 Name(Print Clearly...

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Page 1 10/18/2011 Name (Print Clearly): Student Number: MTH132 Section 5 & 18, Quiz 7 Nov 24, 2008 Instructor: Dr. W. Wu Instructions: Answer the following questions in the space provided. There is more than adequate space provided to answer each question. The total time allowed for this quiz is 15 minutes. 1. [3 pts each] . Evaluate the integrals . (a) + 1 0 2 ) ( dx x x 1 3 2 3 1 0 1 3 2 1 3 1 ) 3 2 3 1 ( 2 / 3 3 1 0 2 / 3 3 | = + = - + = + x x (b) - + 2 / 2 / 2 ) sin 8 ( π π dy y y + = + - - 2 / 0 2 2 / 2 / 2 / 2 / 2 0 16 sin 8 π π π π π dy y dy y dy y (by Symmetry) 3 3 2 / 0 3 3 2 0 8 3 1 16 3 1 16 | π π π = - = = y 2. Find the derivative of x tdt dx d 0 cos . (a)[2 pts] by evaluating the integral and differentiating the result ) sin( 0 sin ) sin( sin cos | 0 0 x x t tdt x x = - = = x x x dx d x x dx d 2 ) cos( ) cos( ) sin( = = (b)[2 pts] by using FTC part I. 2 / 1 0 2 1 ) cos( )' ( ) cos( cos - = = x x x x tdt dx d x

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Page 2 10/18/2011 (c)[bonus 2 pts] Find x dt t x x + 0 2 0 ) cos( lim . x dt t x x + 0 2 0 ) cos( lim ( 0 0 , then use L’H Rule) = 1 cos lim )' ( )' ( ) cos( lim 0 0 = = + + x x x x x x (Use FTC part I) 3. [4 pts]. Find the total area between the x-axis and the curve of x x y 2 2 - - = , 2 3 - x . ( x x y 2 2 - - = could be negative, so we must consider subintervals where the function does not change sign)
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MTH132-Quiz7-Solutions (1) - Page 1 Name(Print Clearly...

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