Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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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.
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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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