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
Solve by parts
![The image contains a mathematical problem involving the integration of the inverse sine function. Here’s the transcription:
---
**Problem:**
\[ c) \quad \int \sin^{-1}(x) \, dx \]
*Written next to it in red ink: "by parts," indicating the use of integration by parts to solve the integral.*
---
**Solution:**
The solution begins with setting up integration by parts:
\[ \int \sin^{-1}(x) \, dx \]
It proceeds with:
\[ = \int \sin(x) \, dx + C \]
After simplification, it concludes with:
\[ = -\cos(x) + C \]
*The final answer is circled to emphasize the result.*
---
This example illustrates applying integration techniques, particularly integration by parts, to find the integral of inverse trigonometric functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2e6f77a4-2bfc-4d58-b6c2-577005b77990%2F0fed168b-a11b-498f-a732-8e18c40f775d%2Fimm3odd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains a mathematical problem involving the integration of the inverse sine function. Here’s the transcription:
---
**Problem:**
\[ c) \quad \int \sin^{-1}(x) \, dx \]
*Written next to it in red ink: "by parts," indicating the use of integration by parts to solve the integral.*
---
**Solution:**
The solution begins with setting up integration by parts:
\[ \int \sin^{-1}(x) \, dx \]
It proceeds with:
\[ = \int \sin(x) \, dx + C \]
After simplification, it concludes with:
\[ = -\cos(x) + C \]
*The final answer is circled to emphasize the result.*
---
This example illustrates applying integration techniques, particularly integration by parts, to find the integral of inverse trigonometric functions.
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