Explanation Given information: Given definite integral is ∫ 0 2 ( 12 x 2 + 1 ) d x . Calculation: Solving the indefinite integral: ∫ ( 12 x 2 + 1 ) d x The antiderivative of a function of the form ( a + b ) is given by ∫ ( a + b ) d x = ∫ a d x + ∫ b d x The antiderivative of a function of the form x n is given by ∫ x n d x = x n + 1 n + 1 + C where n â‰ -1 The antiderivative of a constant a is given by ∫ a d x = a x + c Using the above-mentionedrules, ∫ ( 12 x 2 + 1 ) d x = ∫ 12 x 2 d x + ∫ 1 d x ∫ ( 12 x 2 + 1 ) d x = 12 ∫ x 2 d x + ∫ 1 d x ∫ ( 12 x 2 + 1 ) d x = 12 ( x 2 + 1 2 + 1 ) + x + C ∫ ( 12 x 2 + 1 ) d x = 12 ( x 3 3 ) + x + C ∫ ( 12 x 2 + 1 ) d x = 4 ( x 3 ) + x + C ∫ ( 12 x 2 + 1 ) d x = 4 x 3 + x + C Where C is a constant

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 6.3, Problem 4P

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To evaluate the definite integral using the Fundamental Theorem.

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Chapter 6.3, Problem 3P

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Chapter 6 Solutions

APPLIED CALCULUS (WILEY PLUS)

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To evaluate the definite integral using the Fundamental Theorem.

Solution Summary: The author evaluates the definite integral using the Fundamental Theorem.

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Chapter 6 Solutions