COS X To check for the result, prove that CSC X+ 1- cos x xp Evaluate the lee cida nE the onuntion

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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Please answer this part of the equation. Make sure each step done is correct and you show each step being done nicely and clearly. ( do the one that’s blank)
-sc x +=1- cos²x
COS X
To check for the result, prove that.
dx
- cos?x
Evaluate the left side of the equation.
CSC X +
= CSC X
dx
COS X
sin x
COS X
COS X
Transcribed Image Text:-sc x +=1- cos²x COS X To check for the result, prove that. dx - cos?x Evaluate the left side of the equation. CSC X + = CSC X dx COS X sin x COS X COS X
Find the indefinite integral and check the result by differentiation.
COS X
dx
1 cos?x
Step 1
First, solve the denominator of the integrand. Recall that
sin2x + cos2x
X =
Step 2
Therefore, rewrite the integrand.
COS X
COS X
1 Cos-x
= xp
dx
sin
sin (r)
Rewrite the right side as a product of two fractions and evaluate the integral. (Use C for the constant of integration.)
COS X
sin x
sin x
sin(r)
xp
cse(x)
Csc(r) (cot x) dx
CSC x + C
csc(z)
Transcribed Image Text:Find the indefinite integral and check the result by differentiation. COS X dx 1 cos?x Step 1 First, solve the denominator of the integrand. Recall that sin2x + cos2x X = Step 2 Therefore, rewrite the integrand. COS X COS X 1 Cos-x = xp dx sin sin (r) Rewrite the right side as a product of two fractions and evaluate the integral. (Use C for the constant of integration.) COS X sin x sin x sin(r) xp cse(x) Csc(r) (cot x) dx CSC x + C csc(z)
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