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8. Evaluate the integrals below. a) 27 3 •3√x X. dx b) 2 (80x√x + = 17) dx = (1+²+3 -1 2 X x-3 + +27 2₂ )dx N

8. Evaluate the integrals below. a) 27 3 •3√x X. dx b) 2 (80x√x + = 17) dx = (1+²+3 -1 2 X x-3 + +27 2₂ )dx N

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 8: Evaluate the Integrals Below** a) \(\int_{1}^{27} \frac{3}{x \cdot \sqrt[3]{x}} \, dx\) b) \(\int_{\frac{1}{4}}^{1} \left( 80x\sqrt{x} + \frac{1}{x^2} \right) \, dx\) c) \(\int_{-1}^{2} \left( \frac{-1}{x-3} + \frac{2}{x+2} \right) \, dx\) **Explanation:** The exercise provides three definite integrals for evaluation. Each integral has specific limits of integration and involves different algebraic expressions. These integrals may require substitution, integration by parts, or partial fraction decomposition to solve, depending on the specific form of the integrand. The task is to apply integration techniques to find the exact values of these integrals within the given limits.
Transcribed Image Text:**Question 8: Evaluate the Integrals Below** a) \(\int_{1}^{27} \frac{3}{x \cdot \sqrt[3]{x}} \, dx\) b) \(\int_{\frac{1}{4}}^{1} \left( 80x\sqrt{x} + \frac{1}{x^2} \right) \, dx\) c) \(\int_{-1}^{2} \left( \frac{-1}{x-3} + \frac{2}{x+2} \right) \, dx\) **Explanation:** The exercise provides three definite integrals for evaluation. Each integral has specific limits of integration and involves different algebraic expressions. These integrals may require substitution, integration by parts, or partial fraction decomposition to solve, depending on the specific form of the integrand. The task is to apply integration techniques to find the exact values of these integrals within the given limits.
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