Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Question
Solve with u substitution.
The image displays handwritten mathematical work on integration. Let's break it down: 1. The problem presented is the integral of the function \(6\sin^6(x)\cos(x) \, dx\). 2. There is a note in red, possibly indicating a substitution hint: "u = sin(x)". 3. The solution process: - The integral \(\int 6\sin^6(x)\cos(x) \, dx\) is considered. - The process seems to involve a substitution, as implied by the red annotation. - The expression \(\int 6\sin^{6+1}(x) \, dx\) suggests that the power of sine is incremented by one as part of the integration process. - The integration result seems to be \(-\frac{6\cos^7}{7}\), indicating the final form of the antiderivative. 4. Below, there is part of another integral, but it is not clearly shown in the image snippet provided. This document appears to be an example of solving an integral using substitution, demonstrating concepts of calculus and integration.
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Transcribed Image Text:The image displays handwritten mathematical work on integration. Let's break it down: 1. The problem presented is the integral of the function \(6\sin^6(x)\cos(x) \, dx\). 2. There is a note in red, possibly indicating a substitution hint: "u = sin(x)". 3. The solution process: - The integral \(\int 6\sin^6(x)\cos(x) \, dx\) is considered. - The process seems to involve a substitution, as implied by the red annotation. - The expression \(\int 6\sin^{6+1}(x) \, dx\) suggests that the power of sine is incremented by one as part of the integration process. - The integration result seems to be \(-\frac{6\cos^7}{7}\), indicating the final form of the antiderivative. 4. Below, there is part of another integral, but it is not clearly shown in the image snippet provided. This document appears to be an example of solving an integral using substitution, demonstrating concepts of calculus and integration.
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