Explanation Given information: Given definite integral is ∫ 0 2 ( 3 t 2 + 4 t + 3 ) d t . Calculation: Solving the indefinite integral: ∫ ( 3 t 2 + 4 t + 3 ) d t 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, ∫ ( 3 t 2 + 4 t + 3 ) d t = ∫ 3 t 2 d t + ∫ 4 t d t + ∫ 3 d t ∫ ( 3 t 2 + 4 t + 3 ) d t = 3 ∫ t 2 d t + 4 ∫ t d t + 3 ∫ 1 d t ∫ ( 3 t 2 + 4 t + 3 ) d t = 3 ( t 2 + 1 2 + 1 ) + 4 ( t 1 + 1 1 + 1 ) + 3 t + c ∫ ( 3 t 2 + 4 t + 3 ) d t = 3 ( t 3 3 ) + 4 ( t 2 2 ) + 3 t + c ∫ ( 3 t 2 + 4 t + 3 ) d t = t 3 + 2 t 2 + 3 t + c Where C is a constant

6th Edition

ISBN: 9781119275565

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 6.3, Problem 5P

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To evaluate the definite integral using the Fundamental Theorem.

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Chapter 6.3, Problem 4P

Chapter 6.3, Problem 6P

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Chapter 6 Solutions

APPLIED CALCULUS-PRINT COMPANION (LL)

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To evaluate the definite integral using the Fundamental Theorem.

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Chapter 6 Solutions