Home
Class 12
MATHS
int(x^(49)tan^(-1)(x^(50)))/((1+x^(100))...

`int(x^(49)tan^(-1)(x^(50)))/((1+x^(100)))dx=k[tan^(-1)(x^(50))]^(2)+C,` , then k is equal to

A

`(1)/(50)`

B

`-(1)/(50)`

C

`(1)/(100)`

D

`-(1)/(100)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `l=intx^(49)(tan^(-1)(x^(50)))/(1+(x^(50))^(2))dx`
Put`" "x^(50)=t" "rArr" "50x^(49)dx=dt`
`therefore" "l=(1)/(50)int(tan^(-1)t)/(1+t^(2))dt`
Again, put `tan^(-1)t=u rArr (1)/(1+t^(2))dt=du`
`therefore" "l=(1)/(50)int u du =(u^(2))/(100)+C=((tan^(-1)x^(50)))/(100)+C`
`"But "l=k(tan^(-1)x^(50))^(2)+C" [given]"`
`therefore" "k=(1)/(100)`
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_( then k)^( if )(x^(49)tan^(-1)(x^(50)))/(1+x^(100))dx=k*[tan^(-1)(x^(50))]^(2)+c

int_( then )^((x^(49)tan^(-1)x^(50))/(1+x^(100)))1+x^(100)dx=k[tan^(-1)(x^(50))]^(2)+C

int(x^(2)tan^(-1)x)/(1+x^(2))dx

inte^(x){tan^(-1)x+(1)/((1+x^(2)))}dx=?

If int((x^(2)-1)dx)/((x^(4)+3x^(2)+1)Tan^(-1)((x^(2)+1)/(x)))=klog|tan^(-1)""(x^(2)+1)/x|+c , then k is equal to

int((tan^(-1)x)^(3))/(1+x^(2))dx is equal to

inte^x(tan^-1x+1/(1+x^(2)))dx

int(tan^(-1)x+x+tan^(-1)((1)/(x)))dx =