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Exam 3 Review Answers

Exam 3 Review Answers - Math 150A Midterm Exam 3 Review...

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Midterm Exam 3 Review – Answers 1. Use the definition of the definite integral to evaluate the following: + + 2 0 2 ) 1 2 3 ( dx x x Use the right endpoints of the subintervals for your sample points. Dividing the interval [0, 2] into n equal subintervals, we have n n x 2 0 2 = - = , n i x i x i 2 0 = + = , 1 4 12 1 2 2 2 3 1 2 3 ) ( 2 2 2 2 + + = + + = + + = n i n i n i n i x x x f i i i , and n n i n i n n i n i x x f i 2 8 24 2 1 4 12 ) ( 2 3 2 2 2 + + = + + = + + = + + = + + = = = = n i n i n i n n i n n n i n i n n i n i dx x x 1 1 2 1 3 2 1 2 3 2 2 0 2 2 8 24 lim 2 8 24 lim ) 1 2 3 ( + + + + + = + + = = = = n n n n n n n n n n i n i n n n i n i n i n 2 2 ) 1 ( 8 6 ) 1 2 )( 1 ( 24 lim 1 2 8 24 lim 2 3 1 1 2 1 2 3 14 2 ) 1 ( 4 ) 2 ( 4 2 ) 1 ( 4 ) 1 2 )( 1 ( 4 lim 2 3 = + + = + + + + + = n n n n n n n n 2. What, exactly, does b a dt t f ) ( mean? Divide the interval [ a , b ] into n subintervals, with a = x 0 , x 1 , . . ., x n -1 , x n = b being the endpoints of the subintervals. For each subinterval, let Δ x i = x i x i -1 be the width of that subinterval, and choose x i * , x i -1 x i * x i , as the sample point for that subinterval. Then, = = n

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Exam 3 Review Answers - Math 150A Midterm Exam 3 Review...

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