Choose the correct answer.
The value of the integral $\int_{\frac{1}{3}}^{1} \frac{\left(x-x^{3}\right)^{\overline{3}}}{x^{4}} d x$ is
(A) 6
(B) 0
(C) 3
(D) 4

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 9

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Video Transcript

problem number nine in which we need to solve and select the options. Okay, so this is from one by 3 to 1. One by 3 to 1. X minus. Excuse me. That is really about one by three, divide by x rays depart for. Okay, so we have to just substitute X equal to 10 theatre. If we substitute X equals sorry, X equal to sine theta. So D X will be equal to of course the to the theater. Now limits when X equal to one by three mm mm So theater will be equal to sign in verse one by three and when X equal to 13 to will be equal to bye bye to. So transformation will be sign universe one by three. One by three. And bye bye. Two. Okay and this is X minus X. Batteries to exit scientist to minus sci Q. T. To raise the power one by three by signed for theater and D excess because tita tita. Okay, so we should just write it as uh huh sign in verse one by three. And by by two we could write it as science. Theater is to the power one by three. Science to to raise to the power one by three into one of mine is caused. It is of course is quite bitter. It will become of course theater is to the power two by three. Bye. Science quality to and to science quality to and it should be called theater the theater which means sign in verse one by three to buy way too. If you look at it the powers the exponents of all it will be it will come out to be co theater raised to the power one by certified by three five by three divided by scientific to raise their power five by three in two Kosik square theater. The theater. So this is a sine inverse. And by three. Bye bye to this will be caught peter is to the power five by three because it is quite a bit. So if you plug in cost it equal to sorry court protocol duty car theater equal to T. So minus Corsica square theater. The theater will be equal to D. T. And the limits when this is called when the take well to sign was won by three. So T will be equal to to route to a month later bye bye to the will be equal to zero. So limit will change too. Science Universal to go to 22 from zero and it will be T raised to the power five by three and GT. So this will be seriously power five by three plus one. Eight by three by eight by three from 2220 So this is three by eight zero. Okay. Mhm. To to Yes 2220 So uh Rebate minus. Okay. Mhm. Okay. I have missed a minus here because this is minus cosine squared theta minus minus minus so minus zero minus. Uh Too rude to raise to the power eight by three, so this will be minus minus plus three by eight into tourists. To this is two raised to the power three by two in 28 by three. So for three by 18 to 16, so six will be the answer, 60 dancing and correct option is a thank you.

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