Explanation Formula Used: If a and b are constants and f(x) and g(x) are continuous functions on [a, b], then: Linear property of integrals: ∫ ( a f ( x ) + b g ( x ) ) d x = a ∫ f ( x ) d x + b ∫ g ( x ) d x And ∫ x n d x = x n + 1 n + 1 + C And the Fundamental theorem of calculus: ∫ a b f ( x ) d x = F ( b ) − F ( a ) , where F ′ ( x ) = f ( x ) Calculations: First find the indefinite integral, ∫ ( 12 x 3 − 3 x 2 ) d x . From the linear property and the above formula, the given integral can be written as, ∫ ( 12 x 3 − 3 x 2 ) d x = 12 ∫ x 3 d x − 3 ∫

4th Edition

ISBN: 9781319434540

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 5, Problem 44CRE

To determine

To evaluate: The integral given below

$\int_{0}^{2} (12 x^{3} - 3 x^{2}) d x$

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Chapter 5, Problem 43CRE

Chapter 5, Problem 45CRE

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Chapter 5 Solutions

ACHIEVE STANDALONE ACCESS F/ CALC 4E

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The integral given below ∫ 0 2 ( 12 x 3 − 3 x 2 ) d x

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Chapter 5 Solutions

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