Integrate the functions.
$$
\sqrt{1-4 x-x^{2}}
$$

Answer

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Calculus 2 / BC

NCERT Class 12 Part 2 - Math

Chapter 7

Integrals

Section 7

Definite Integral

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Video Transcript

Hello we have problem number five and which? We need to integrate? One minus four X minus x squared. And the route one minus four x minus that square on the road. Now let us first completed square so let us take minus as common. So it will become forex mine for exploits. Access choir under route. So this is one minus x plus two whole square minus four under the square root. So one minus X plus two whole Squire plus four under the square root. So four plus 15 under five whole square minus express to whole square. Underwrote. We have integrated. So let us right I equal to integration of I wrote five whole square minus explains to hold square under the square root dx. Now if you substitute X plus two equal to Y so D X will be equal to Dy Yeah, so this will become that would favor or square minus y squared a little dy Okay, so this is in the form of access square minus where access square mindset is quite under route. So uh yes, Goldman Sachs Square. So this is in the form of a square minus x squared and the root dx. This is formula this which he calls to one by two X a square minus X squared plus a square by two. Signing worse X by a policy. Now, X by policy. So here why is in place of X and route five is in place of a So I will be able to one by two access Y a square mine sex square. That is five minus Y squared plus a squared by two. Five by two. Sign universe X by a Why Buy road five policy. Now let's plug in the value of Y S X plus two. So this will be experts two by two and the road. If we just write what I call the explains to and so it will be one minus four X minus x squared. So this is one minus four x minus six square place five by two. Sign Universe X plus two by under five plus C. So this should be the answer. Okay, so this is answer for fifth question. Thank you.

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