Explanation Given Information: The provided definite integral is; ∫ 3 6 x 4 x − 7 d x Formula used: The formula for the integral ∫ u a + b u d u is: ∫ u a + b u d u = 1 b 2 ( b u − a ln | a + b u | ) + C The General power differentiation Rule: d d x [ u n ] = n u n − 1 d u d x Calculation: Consider u = x . Differentiate the considered function with respect to x using power rule of differentiation. d u = d x Consider the provided expression: ∫ 3 6 x 4 x − 7 d x Rewrite. ∫ 3 6 x 4 x − 7 d x = ∫ 3 6 x − 7 + 4 x d x Here, a = − 7 , b = 4 , u = x and d u = d x . Substitute u for x , a for − 7 , b for 4 , and d u for d x as; ∫ 3 6 x 4 x − 7 d x = ∫ 0 5 u a + b u d u Now, use the above integration formula and solve the integral as: ∫ 3 6 x 4 x − 7 d x = [ 1 b 2 ( b u − a ln | a + b u | ) ] 3 6 Substitute x for u , − 7 for a , and 4 for b as; ∫ 3 6 x 4 x

Calculus: An Applied Approach (Providence College: MTH 109)

9th Edition

ISBN: 9781285142616

Author: Ron Larson

Publisher: CENGAGE C

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Chapter 6.2, Problem 39E

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Chapter 6.2, Problem 38E

Chapter 6.2, Problem 40E

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Chapter 6 Solutions

Calculus: An Applied Approach (Providence College: MTH 109)

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The solution of definite integral ∫ 3 6 x 4 x − 7 d x .

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To calculate: The solution of definite integral ∫36x4x−7dx.

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Chapter 6 Solutions