Problem

Integrate the functions. $$ \frac{x+2}{\sqrt{x^{2…

05:33

Problem 20 Easy Difficulty

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

Answer

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Calculus 2 / BC

NCERT Class 12 Part 2 - Math

Chapter 7

Integrals

Section 4

Integrals of some Particular Functions

Discussion

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Video Transcript

We have 1000 number 20 in which we need to integrate express to buy four X minus taxes choir under the squad room. Okay so let us write this as X plus two equal to a D by dx four x minus X squared plus B. So this will become four minus two x into a plus B. So this is -2 x plus G. Place for A. Now if we equate this is X plus two if he could Coefficient of X. So this in mind is to equal to one so they will become equal to minus one by two And if he could constant term AC -1 x two Constant term B plus for equal to two which means we will be equal to 2 -4. A. Okay so two Plus two is 4 so is too eight miles 1 x 24. So this could be done is our deal could be written Nice A which is equal to -1 x two differentiation of this differentiation of for x minus X esquire so four x minus X squared. So we'll be simply writing 4 -2 x divided by back and plus B. That is for mhm divided by four x minus X squared under the square root. So we need to integrate it. Now let us separate it out. It will become -1 x two. 4 -2 weeks by four x minus X choir DX plus four one by four X minus X squared dx. Okay no this is island. This is I took so first of all and a complete die. So for Taiwan we'll be having minus one by two for minus two X. So if we assume if you substitute for ex mine sexist or equal to T So 4 -2 x dx will become DT. So this whole thing is DT So our question becomes our question becomes one x 2. Former Minister that is DT by under duty And this is -1 x two. Tears to the power minds one by two plus one By -1 x two Plus 1. So these two will get cancelled out some mines under duty and plus constant of integration seven. So this solution is minus four x- x esquire Plus seven. Similarly, if you go forward I too it is four one x 4 x- X squandered. So you know just what agent as By taking negative as common access choir -4 x and the road dx. So for one by minus We are completing the Squire, X -2 old square minus two. Study minus four dx. So four, one by and under the square root one before that is to a Squire minus X -2 Whole Square under the Square Root. Now let us substitute X -2 equal to T. So the X will be equal to DT Okay so this becomes equal to 4. 1 by to a Squire minus t square duty. So this is in the form of one by a square minus X squared for a square minus x squared under the square root. We have sign universe X by A. So this is four into Sen University by two Plus C. Mhm. No Liberty is foreign to sign Universe. We have TX -2. My two plus C two. Let's let's right so I will become I one plus I to Yeah. Okay so Ivan is minus four X minus x squared four x minus x squared on the road. And plus four. That's forced by inverse X -2 x two plus seven plus E to let us write combining the at sea. So they should be there for number 20. Thank you so much.

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