Home
Class 12
MATHS
int(x-.^(11)C(1)x^(2)+.^(11)C(2)x^(3)-.^...

`int(x-.^(11)C_(1)x^(2)+.^(11)C_(2)x^(3)-.^(11)C_(3)x^(4)+...-.^(11)C_(x^(12)))dx` equal to

A

`((1-x)^(12))/(12)-((1-x)^(11))/(11)+C`

B

`((1-x)^(13))/(13)-((1-x)^(12))/(12)+C`

C

`((1-x)^(11))/(11)-((1-x)^(12))/(12)+C`

D

`((1-x)^(12))/(12)-((1-x)^(13))/(13)+C`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `l=int x (1-.^(11)C_(1)x+.^(11)C_(2)x^(2)-.^(11)C_(3)x^(3)+…..-.^(11)C_(11)x^(11))dx`
`=int x(1-x)^(11)dx`
`"Put "1-x=t`
`therefore" "dx=-dt`
`"Then, "l=- int(1-t)t^(11)dt=-(t^(12))/(12)+(t^(13))/(13)+C`
`=((1-x)^(13))/(13)-((1-x)^(12))/(12)+C`
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|30 Videos

  • INTEGRATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|30 Videos

  • FACTORIZATION FORMULAE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2|21 Videos

  • LINE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|3 Videos

Similar Questions

Explore conceptually related problems

int x^(11)dx

int(x^2-x^11)dx

(.1^(11)C_(0))/(1)+(.^(11)C_(1))/(2)+(.^(11)C_(2))/(3)+....+(.1^(11)C_(10))/(11)

The value of |(.^(10)C_(4).^(10)C_(5).^(11)C_(m)),(.^(11)C_(6).^(11)C_(7).^(12)C_(m+2)),(.^(12)C_(8).^(12)C_(9).^(13)C_(m+4))| is equal to zero when m is

int(11x-18)/(x^(11)(6sqrt(x^(12)-2x+3)))dx is equal to

(11C_(0))/(1)+(11C_(1))/(2)+(11C_(2))/(3)+......+(11C_(10))/(11)=

int(3x^(13)+2x^(11))/((2x^(4)+3x^(2)+1)^(4))dx

int_(0)^(11)((11-x)^(2))/(x^(2)+(11-x)^(2))dx=