Explanation Given: ∫ ( 2 x − 1 ) x 2 e 2 x d x Concept used: ∫ e x [ f ( x ) + f ′ ( x ) ] d x = e x f ( x ) + C Calculation: The given integral can be evaluated as Put 2 x = t ⇒ 2 d x = d t ⇒ d x = d t 2 ∴ ∫ ( 2 x − 1 ) x 2 e 2 x d x = ∫ t − 1 ( t 2 ) 2 e t d t 2 = 2 ∫ t − 1 t 2 e t d t = 2 ∫ e t ( t t 2 − 1 t 2 ) d t &

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 7.2, Problem 56PS

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To evaluate the integral ∫( 2x−1) x 2 e2x dx

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Chapter 7.2, Problem 55PS

Chapter 7.2, Problem 57PS

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x-1 4). L141 dx x²+1

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Approximate the value(s) of x that satisfies the equation lnx =x2 −1.

Chapter 7 Solutions

Calculus

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To evaluate the integral ∫ ( 2 x − 1 ) x 2 e 2 x d x

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To evaluate the integral ∫( 2x−1) x 2 e2x dx

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Chapter 7 Solutions