Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
Can you explain to me on the following problem how you convert theta to arc sin for the answer please solve # 137
## Completing the Square and Trigonometric Substitution ### Completing the Square Use the technique of completing the square to express each trinomial as the square of a binomial. 131. \(4x^2 - 4x + 1\) 132. \(2x^2 - 8x + 3\) 133. \(-x^2 - 2x + 4\) ### Trigonometric Substitution Integrate using the method of trigonometric substitution. Express the final answer in terms of the variable. 134. \(\int \frac{dx}{\sqrt{4 - x^2}}\) 135. \(\int \frac{dx}{\sqrt{x^2 - a^2}}\) 136. \(\int \sqrt{4 - x^2} \, dx\) 137. \(\int \frac{dx}{\sqrt{1 + 9x^2}}\) 138. \(\int \frac{x^2 \, dx}{\sqrt{1 - x^2}}\) There are no graphs or diagrams included in this content. Some exercises are highlighted in color, which might indicate their importance or that they are to be given special attention in solving.
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Transcribed Image Text:## Completing the Square and Trigonometric Substitution ### Completing the Square Use the technique of completing the square to express each trinomial as the square of a binomial. 131. \(4x^2 - 4x + 1\) 132. \(2x^2 - 8x + 3\) 133. \(-x^2 - 2x + 4\) ### Trigonometric Substitution Integrate using the method of trigonometric substitution. Express the final answer in terms of the variable. 134. \(\int \frac{dx}{\sqrt{4 - x^2}}\) 135. \(\int \frac{dx}{\sqrt{x^2 - a^2}}\) 136. \(\int \sqrt{4 - x^2} \, dx\) 137. \(\int \frac{dx}{\sqrt{1 + 9x^2}}\) 138. \(\int \frac{x^2 \, dx}{\sqrt{1 - x^2}}\) There are no graphs or diagrams included in this content. Some exercises are highlighted in color, which might indicate their importance or that they are to be given special attention in solving.
Expert Solution
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Step 1

The given integral is as follows.

∫dx1+9x2

Rewrite the integral is ∫dx1+3x2

Substitute,3x = sinh θ

 3x = sinh θx=sinhθ3

Find the derivative.

x=sinhθ3dx=13coshθ

 

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