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Evaluate the integral. Check your result by differentiation. (Use C for the constant of integration.) 2)42x dx

Evaluate the integral. Check your result by differentiation. (Use C for the constant of integration.) 2)42x dx

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
### Problem Statement Evaluate the integral. Check your result by differentiation. (Use \( C \) for the constant of integration.) \[ \int (x^2 + 2)^4 2x \, dx \] ### Explanation Upon evaluating this integral, use the chain rule and substitution method. The term inside the integral may suggest considering the substitution \( u = x^2 + 2 \). After substituting, integrate, and simplify the expression. Finally, differentiate to ensure that you arrive back at the original integrand, confirming the correctness of the solution. **Note:** The blank rectangle below the problem statement is usually for the final answer or additional notes.
Transcribed Image Text:### Problem Statement Evaluate the integral. Check your result by differentiation. (Use \( C \) for the constant of integration.) \[ \int (x^2 + 2)^4 2x \, dx \] ### Explanation Upon evaluating this integral, use the chain rule and substitution method. The term inside the integral may suggest considering the substitution \( u = x^2 + 2 \). After substituting, integrate, and simplify the expression. Finally, differentiate to ensure that you arrive back at the original integrand, confirming the correctness of the solution. **Note:** The blank rectangle below the problem statement is usually for the final answer or additional notes.
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