Explanation Given Information: The provided integral is ∫ x e 2 x 2 d x . Formula used: If u is a function of x , then: ∫ e u ⋅ u ′ d x = ∫ e u d u = e u + C Calculation: Consider the provided integral: ∫ x e 2 x 2 d x Rewrite the integral by multiplying and dividing by 4 as: 1 4 ∫ 4 x e 2 x 2 d x Now, consider u = 2 x 2 . Then, the above integral became as, 1 4 ∫ 4 x e u d x Now, use the formula of integral: ∫ e u ⋅ u ′ d x =

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Chapter 12.3, Problem 10E

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To calculate: The value of the integral ∫xe2x2dx.

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Chapter 12.3, Problem 9E

Chapter 12.3, Problem 11E

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Chapter 12 Solutions

MATHEMATICAL APPLICATIONS FOR PKG

Ch. 12.1 - 1. True or false: (a) (b) Ch. 12.1 - Prob. 2CP Ch. 12.1 - 1. If what is Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Prob. 7E Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...

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The value of the integral ∫ x e 2 x 2 d x .

Solution Summary: The author calculates the value of the provided integral by multiplying and dividing by 4.

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To calculate: The value of the integral ∫xe2x2dx.

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Chapter 12 Solutions