Explanation Approach: The integration of by parts ∫ u d v = u v − ∫ v d u Here u ( x ) and v ( x ) differential function. Calculation: Consider the given integration, ∫ ( 3 x 2 + 4 ) e 2 x d x . Let u = 3 x 2 + 4 and d v = e 2 x d x . Then d u = 6 x d x Found the v by integrating the function d v = e 2 x d x : ∫ d v = ∫ e 2 x d x After integration: v = e 2 x 2 = 1 2 e 2 x Substitute 1 2 e 2 x for v , e 2 x d x for d v , 6 x d x for d u and 3 x 2 + 4 for u in the ∫ u d v = u v − ∫ v d u : ∫ ( 3 x 2 + 4 ) e 2 x d x = ( 3 x 2 + 4 ) ( 1 2 e 2 x ) − ∫ ( 1 2 e 2 x ) 6 x d x = 1 2 ( 3 x 2 + 4 ) e 2 x − 3 ∫ e 2 x x d x Now apply integration by parts to the last integration letting, Let u = x and d v = e 2 x d x Then, d u = d x

2nd Edition

ISBN: 9780321964458

Author: Lial

Publisher: PEARSON EDUCATION (COLLEGE)

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Chapter 8.2, Problem 3YT

To determine

To find:

The integration ∫(3x2+4)e2xdx.

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Chapter 8.2, Problem 2YT

Chapter 8.2, Problem 4YT

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EBK CALCULUS FOR THE LIFE SCIENCES

Ch. 8.1 - YOUR TURN Use the trapezoidal rule with n=4 to...Ch. 8.1 - Prob. 2YT Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E

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