Problem

Give the proper trigonometric substitution and fi…

Problem 6 Easy Difficulty

Give the proper trigonometric substitution and find the transformed integral, but do not integrate.
$$\int \frac{d x}{\left(1-x^{2}\right)^{3 / 2}}$$

Answer

$x=\sin \theta, \quad \int \sec ^{2} \theta d \theta$

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Calculus 1 / AB

Basic Technical Mathematics with Calculus

Chapter 28

Methods of Integration

Section 8

Integration by Trigonometric Substitution

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Video Transcript

in this question they'll give an integration either. I can say that wonder why did why one minus access were raised to the power three baidu and the expo. Okay let it I denote by I we can see that the form here is square root of one is where minus access. We're okay. And in this form you know that the proper substitution is a science data and you see in your case at the place of we have one so I'm going to make your substitution of X by science data. It shows that it's a dairy or you can be written as costs it our duty to now make this tablet replacements clearly. So see we're here one upon we have one minus sine squared. Theta raised to the power three by two and the X. Is replaced by cost data data data. Okay further one mind sinus square theater changes into bosses square feet to raise to the power three by two and consider to be data. Okay. No they make the product of powers. Here's solider tear cause guild theater and in the enumerated Costa to the theater. After the cancellation of the cost theater we have in the denominator remain with one of bone causes square theater. Okay. The theater, you know that one of one cause theater is set theater. So I got the simplest form of the integration that is sexy Square theater. The theater. Okay. This is the simplest form that was asked in the question and you can see that for to get this in place from. What I had done here is that I had to replace X by scientific to hear. Okay. Thank you.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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