Explanation Given information : The given integral is I = ∫ e x e x / 3 + e x / 2 d x Formula used : I = ∫ x n d x = x n + 1 n + 1 + C , and ∫ d x x = log e x + C where C is the constant of integration . Calculations: We evaluate given integral by substitution method I = ∫ e x e x / 3 + e x / 2 d x ...... (1) Now, let e x = t 6 ⇒ e x d x = 6 t 5 d t . Substituting values e x and e x d x in result (1), we have I = ∫ 6 t 5 d t t 2 + t 3 =6 ∫ t 3 d t t + 1 = 6 ∫ ( t 3 + 1-1 ) d t t + 1 = 6 ∫ ( t 3 + 1 ) d t t + 1 -6 ∫ d t t + 1 ⇒ I = 6

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J

Publisher: Kendall Hunt Publishing

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Chapter 7, Problem 43SP

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Toevaluate:The given integral I=∫ e x e x/3+ e x/2dx .

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Chapter 7, Problem 42SP

Chapter 7, Problem 44SP

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Chapter 7 Solutions

Student's Solution and Survival Manual for Calculus

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Toevaluate: The given integral I = ∫ e x e x / 3 + e x / 2 d x .

Solution Summary: The author evaluates the given integral by substitution method I=displaystyle int

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Toevaluate:The given integral I=∫ e x e x/3+ e x/2dx .

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Chapter 7 Solutions