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Integrate each of the given functions.$$\int_{0}^{0.5} \frac{x^{3} d x}{\sqrt{1-x^{2}}}$$

$\frac{2}{3}-\frac{3 \sqrt{3}}{8}$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 8

Integration by Trigonometric Substitution

Integrals

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Hello everyone today we'll solve the integral from 0 to 15 of Execute or wrote of one man x square. Um So this is a the U substitution question where you is one minus expert. Mhm. Do you hands minus two X. And you can write X square as one minute you are you getting that into the formula? Um So for now just forget about the are lower and upper bound homelessness on the integral as it is. So integration of without the lower and profound wonderful 11 issue. So we have 190 x into x square over. You don't talk one minutes expert. You can write this as expire if you wonder if you into X over route of you because of that experience you into 30 years here joe Yes can recognize do you? Mhm minus directs his access cancel out but in the end you get -1 or tow dignity constant out of the interview one man issue. Oh for sure yeah. Do you you can mind that I'm not using the upper and lower bounds still I keep put this in terms of X again so integrating it normally you could get you can know this as Integration of one over with you minus you wrote you and this can get it as 1/2 and two. The incarnation of directional mind your I mean you wish to when his half minus curious to off mm this you can integrate within the laws of integration judge you raised one nice half past one one minutes half cash one flash you get your talk well This one for half blessed one and damn can To interpret the integrating this you can write one or 2. Funny you raised her. Uh huh for half play this areas to three x 2 or three x 2. Now you can simplify this further um by writing it as when it's half. Thank you to you awareness two by three because you killed and now I want you want you want to buy myself into the brackets and open the brackets. You get minus Rukia. Yes you killed only three. I know you need to replace us. Uh that's us one minute 6 square as we are taking it as one man is expired here. You just need to please get back and now I'm going to bring in the uh huh the upper and lower bounds and this giving you one month extra off one minute extra cuba whole wrote on twitter ranging from 0.5. You just write a check. Okay? Yeah these are playing bye. I'm here to the Ukraine five and now when you practice in this situation we should get two by three minus three groups three over. Mhm. And that is your final answer. I hope you guys understood that that this was just a simple use institution. I need to use the U. Sub and play around with expert on you. And I could have changed the upper and lower bounds, but I thought it would be easier to keep it as it is and bring the upper and lower bounds at the very end. Um And the that should be do you over here, do you over here? That's that's your integrating in terms of you. So because I'm sure that, and thanks for watching.

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