Explanation Given: ∫ 7 1 − ( 2 x ) 2 d x Concept Used: ∫ a f ( x ) d x = a ∫ f ( x ) d x d d x x n = n x n − 1 d d x ( sin − 1 x ) = 1 1 − x 2 ∫ 1 1 − x 2 d x = sin − 1 x + C , where C is an arbitrary constant. Calculation: To solve the integrals ∫ 7 1 − ( 2 x ) 2 d x First use substitution by putting 2 x = u ⇒ d ( 2 x ) = d u ⇒ 2 d x = d u ⇒ d x = d u 2 Thus given integral changes as ∫ 7 1 − ( 2 x ) 2 d x = ∫ 7 1 − u 2 d u 2 = 7 2 ∫ 1 1 − u 2 d u Now use fundamental formulae of integrals to solve it further, as 7 2 ∫ 1 1 − u 2 d u = 7 2 s i n − 1 u + C Where C is an arbitrary constant

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 4.4, Problem 39S

To determine

To solve the integrals

∫7 1− ( 2x ) 2 dx

And also check the answer by differentiating.

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Chapter 4.4, Problem 38S

Chapter 4.4, Problem 40S

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To solve the integrals ∫ 7 1 − ( 2 x ) 2 d x And also check the answer by differentiating.

Solution Summary: The author explains how to solve the integrals, using substitution, and checking the answer by differentiating.

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To solve the integrals

∫7 1− ( 2x ) 2 dx

And also check the answer by differentiating.

Want to see the full answer?

Chapter 4 Solutions

To solve the integrals ∫ 7 1 − ( 2 x ) 2 d x And also check the answer by differentiating.

Solution Summary: The author explains how to solve the integrals, using substitution, and checking the answer by differentiating.

Videos

To solve the integrals ∫7 1− ( 2x ) 2 dx And also check the answer by differentiating.

Want to see the full answer?

Chapter 4 Solutions

To solve the integrals

∫7 1− ( 2x ) 2 dx

And also check the answer by differentiating.