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Evaluate the integral using substitution and then Integration by Parts: Leve = x ² ) dx (Hint: Let u =

Evaluate the integral using substitution and then Integration by Parts: Leve = x ² ) dx (Hint: Let u =

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
Evaluate the integral using substitution and then Integration by Parts: Leve 1 dæ (Hint: Let u = x ² ) Evaluate using long division first to write f (x) as the sum of a polynomial and a proper rational function: x³ +1 +1 -dx 3) The solid S obtained by rotating the region below the graph of y = x-¹ about the x-axis for 1 ≤ x < ∞ is called Gabriel's Horn (Figure 11). 1 A = 2π p∞ y=x²l FIGURE 11 (a) Use the Disk Method (Section 6.3) to compute the volume of S. (Note that the volume is finite even though S is an infinite region.) (b) It can be shown that the surface area of S is Show that A is infinite. -4 X √1+x dx x
Transcribed Image Text:Evaluate the integral using substitution and then Integration by Parts: Leve 1 dæ (Hint: Let u = x ² ) Evaluate using long division first to write f (x) as the sum of a polynomial and a proper rational function: x³ +1 +1 -dx 3) The solid S obtained by rotating the region below the graph of y = x-¹ about the x-axis for 1 ≤ x < ∞ is called Gabriel's Horn (Figure 11). 1 A = 2π p∞ y=x²l FIGURE 11 (a) Use the Disk Method (Section 6.3) to compute the volume of S. (Note that the volume is finite even though S is an infinite region.) (b) It can be shown that the surface area of S is Show that A is infinite. -4 X √1+x dx x
->4) Show that the circumference of the unit circle is equal to 1 21. -1 √1-x² Evaluate, thus verifying that the circumference is 27. >5) Calculate the Taylor polynomials T₂ (x) and T3 (x) centered at x = a of the function f(x) = sin x for the given value of a. (a) a = 0 (b) a - ㅠ < 2 dx (an improper integral)
Transcribed Image Text:->4) Show that the circumference of the unit circle is equal to 1 21. -1 √1-x² Evaluate, thus verifying that the circumference is 27. >5) Calculate the Taylor polynomials T₂ (x) and T3 (x) centered at x = a of the function f(x) = sin x for the given value of a. (a) a = 0 (b) a - ㅠ < 2 dx (an improper integral)
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