Evaluate the integrals.
$$
\int_{0}^{2} x \sqrt{x+2} \quad\left(\text { Put } x+2=t^{2}\right)
$$

Answer

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Calculus 2 / BC

NCERT Class 12 Part 2 - Math

Chapter 7

Integrals

Section 10

Some Properties of Definite Integrals

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Problem 1

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Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Video Transcript

problem number four and this we need to integrate from 0 to 2 X. And two. Express to understood we have to plug in we have to substitute X plus two equal to the square. Always where we should say. So if you differentiate it will become D X equal to two. Why dy now we have to change the limits to so when X equal to zero that lower limit Y squared is to so wise route to when X equal to two wise to so limit becomes two 22 an ex plus two so X will be equal to buy square minus two into why into two. Y. Dy value this Okay so limited from root to to to this is why why two can be taken outside. So why square or what is the part of four minus two? Y squared delay. So this is two virus to part five by five minus two. I killed by Q about cuba three 222 And let us start plugging the value of the limits. So to upper limit tourist one by five we should take like this. We should right 20 part five minus I wrote to part five minus two or three to raise to power my three and route to raise to the power three. So this will become too one by 52 30 to minus 405 minus two by three. Eight minus 203. Sorry this should be two. Yeah no three is not fair. It should have been two. Uh huh. So this is too 32 by five minus four by 52 minus 16 by three. Bless four by three. The road three. This is 32 by five. Okay that it we're fine. Okay. Okay. Yeah so let us just combine these two so this will be 15 96 minus 80 and there should be no two. There is a okay and if he clubbed these two we will be getting three plus 15 as L. C. M. So this will be minus 12. Route to Place 20. I do too. So two and 2 16 by 15 and plus four. Two by 15. Okay so if you take there's 15 Dubai 15 and 16. Uh huh. Four or two two by 13 into for every Dick. It will be four by 15. Bless under two by 15. Okay, so 15 will be taken out. That's why 15 should not be here. So they should be the answer. Thank you so much.

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