Explanation Given information: The given integral ∫ 1 8 t 2 t + 8 d t is a definite integral. Formula used: The sum rule for indefinite integrals, ∫ ( f ( x ) + g ( x ) ) d x = ∫ f ( x ) d x + ∫ g ( x ) d x The multiples rule for indefinite integrals, ∫ c f ( x ) d x = c ∫ f ( x ) d x When a substitution is performed using differentials the change of variable formula is used. ∫ f ( u ( x ) ) u ' ( x ) d x = ∫ f ( u ) d u Calculation: Suppose that u = t + 8 . Then, d u d t = d ( t + 8 ) d t d u d t = 1 2 t + 8 2 d u = d t t + 8 Before substituting these results into the integral, the limits should be updated. When t = 1 , t + 8 = 1 + 8 u = 9 u = 3 When t = 8 , t + 8 = 8 + 8 u = 16 u = 4 Then, u = t + 8 u 2 = t + 8 t 2 = ( u 2 − 8 ) 2 Hence, the simplifications can be done as follows

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 5, Problem 68CRE

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To find: The value of the definite integral ∫18t2t+8dt .

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Chapter 5, Problem 67CRE

Chapter 5, Problem 69CRE

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The value of the definite integral ∫ 1 8 t 2 t + 8 d t .

Solution Summary: The author calculates the value of the definite integral displaystyle 'underset', which equals 636.5524.

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To find: The value of the definite integral ∫18t2t+8dt .

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Chapter 5 Solutions