1007_Tut4

# 1007_Tut4 - (b) using left end points of intervals 1 2 3 4...

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MATH 1007 A Tutorial #4 Nov 10, 2006 First Name: Last Name: Student No: No Calculators! You must show your work for all questions! 1. [4 marks] Use substititution to ﬁnd the required integrals: (a) Z (4 + x 2 ) 10 (2 x ) dx (b) Z 2 x 4 - 1 (8 x 3 ) dx Hint: Set u = 4 + x 2 Hint: Set u = 2 x 4 - 1 2. [4 marks] Use the Fundamental Theorem of Calculus to solve the fol- lowing questions: (a) Z 4 1 (1 + 6 x ) dx (b) If g ( x ) = Z e x 0 sin 3 t dt , ﬁnd g 0 ( x ). Hint: let u = e x so that dg dx = dg du · du dx 1

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3. [2 marks] Consider the function f ( x ) = 1 x from x = 1 to x = 5. Use 4 approximating rectangles/intervals to give an expression for the area under f (a) using right end points of intervals
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Unformatted text preview: (b) using left end points of intervals 1 2 3 4 5 x x 1 x 2 x 3 x 4 Recall: To use right endpoints, we use A = n X i =1 f ( x i )Δ x , which in this case becomes A = f ( x 1 )Δ x + f ( x 2 )Δ x + f ( x 3 )Δ x + f ( x 4 )Δ x To use left endpoints, we use A = n X i =1 f ( x i-1 )Δ x , which in this case becomes A = f ( x )Δ x + f ( x 1 )Δ x + f ( x 2 )Δ x + f ( x 3 )Δ x Note: You are NOT required to evaluate your expression (leave it as a sum of fractions). 2...
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## This note was uploaded on 03/22/2010 for the course MATH 1007 taught by Professor Unknown during the Fall '07 term at Carleton.

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1007_Tut4 - (b) using left end points of intervals 1 2 3 4...

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