Explanation Given: The total cost of 13 units is $270. And, C ′ ( x ) = 3 2 x − 1 . Formula used: The integration formula: ∫ x n d x = x n + 1 n + 1 + C Calculation: Consider the indefinite integration: ∫ C ′ ( x ) d x = ∫ 3 2 x − 1 d x Substitute ( 2 x − 1 ) as u . Thus, d x = 1 2 d u . Now rewrite the integral: ∫ 3 2 x − 1 d x = 3 2 ∫ u d u So, 3 2 ∫ u d u = 3 2 u 3 / 2

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Chapter 13, Problem 63RE

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Chapter 13, Problem 62RE

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The cost function of C ′ ( x ) = 3 2 x − 1 .

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