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
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c7f32b8-e74c-4eab-a5df-41a31828ca24%2Fb0bd6a77-1c26-489f-bf71-5f03ae0f1e91%2Fdqsxz0gk_processed.jpeg&w=3840&q=75)
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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c7f32b8-e74c-4eab-a5df-41a31828ca24%2Fb0bd6a77-1c26-489f-bf71-5f03ae0f1e91%2F0uchsb_processed.jpeg&w=3840&q=75)
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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