Here we will study the following integrals by using an inverse trigonometric substitution: ∫ 1/((x^2 + a^2) ^(3/2)) dx, ∫ 1/((x^2 + a^2) ^(5/2)) dx. a) Calculate the following integral: ∫cos^3 θdθ (A tiny hint: cos^2 θ + sin^2 θ = 1 )
Here we will study the following integrals by using an inverse trigonometric substitution: ∫ 1/((x^2 + a^2) ^(3/2)) dx, ∫ 1/((x^2 + a^2) ^(5/2)) dx. a) Calculate the following integral: ∫cos^3 θdθ (A tiny hint: cos^2 θ + sin^2 θ = 1 )
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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Here we will study the following integrals by using an inverse trigonometric substitution: ∫ 1/((x^2 + a^2) ^(3/2)) dx, ∫ 1/((x^2 + a^2) ^(5/2)) dx. a) Calculate the following integral: ∫cos^3 θdθ (A tiny hint: cos^2 θ + sin^2 θ = 1 )dx.
b) Use an inverse trigonometric substitution to show that:∫ (1/((x2+a2)^(3/2)) dx = 1/a2 *(x/(√x2 + a2))+ C). ∫ 1/((x^2 + a^2)^(5/2)) dx = (1/a^4)*(x/(√x^2 + a^2))−(1/3) *x^3/((x^2 +a^2)^(3/2))+ C
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