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Answer the given equations related to the indicated examples of this section.In Example 1, how must the integrand be changed in order to havea result of $\sin ^{-1} x+C ?$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 8

Integration by Trigonometric Substitution

Integrals

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Lectures

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In mathematics, precalculu…

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In mathematics, a function…

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Evaluate the integrals by …

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04:51

If you do not know what su…

05:32

Different substitutions

02:34

Show that $\int \frac{-1}{…

06:02

Evaluate $\int\left(\sin ^…

03:01

Trigonometric Substitution…

01:47

01:10

02:47

$$\text { Integration by p…

in discussion. It is told that we're able to make some changes in example number request so that our integration of the function should be signing for sex. Okay so I'm going to make some changes and I'm going to write the integration of one upon square will talk one minor success square Bx. Okay now let's start with this integration. I'm going to make a substitution here and that is I am going to replace access by scientific tire. Okay now we'll see the creative is you can see here scientists derivative is cause data data. So carefully. I'm going to make this replacements letter did not integration by eye. So you can see that what we should get here after making these replacements one divided by one minus sine and square theater. And at the place of the X. We have to substitute cause theatre de theatre. Okay now further see what happens here. Trigonometry. Identity says that square root of one minus sign is worth it to is there and one minus sign is worth it. Again. The bitterness causes were theater and further we have caused to the theater. Okay, now square out. Of course where theater is simply I can say that one divided by cost data. And we have to multiply by cost it also we can cancel our cost you to so we get here one day theater and now we can integrate one with respect to theater and its integration should be close to theatre plus C. Okay, since we are solving an indefinite integration so I add added constant also. Now I'm going to re substitute here. Okay now I'm going to re substitute. You can see that we had taken Your acts of the question by scientific to hear. It means that data must be replaced by signing over six. Okay, so if you make the substitution, I get here signing what sex. Let's see. Okay, this is the answer. And you can see that to get this answer. What tired do you see here that I can say here is integration of one upon square root one minus access where bX. Okay. Thank.

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