Home
Class 12
MATHS
(sqrttan x)/(sinx. cosx)...

`(sqrttan x)/(sinx. cosx)`

Text Solution

Verified by Experts

Let I `=int (sqrttanx)/(sinx.cos x)dx`
Dividing numerator and denominator by `cos^(2)x`, we get
`I=int (((sqrttanx)/(cos^(2)x)))/(((sin x)/(cosx)))dx=int(sqrttan x.sec^(2)x)/(tan x)dx=int (sec^(2)x)/(sqrtx)dx`
Put tan x=1 `therefore sec^(2)xdx=dt`
`therefore I=int (1)/(sqrtt)dt`
`=int t^(-(1)/(2))dt=(t^((1)/(2)))/(1//2)+c=2sqrtt+c=2sqrttanx+c`
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Theory Questions|6 Videos

  • INTEGRATION

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Example For Practice|128 Videos

  • DIFFERENTIATION

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise MCQ|15 Videos

  • LINE

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Multiple choice question|9 Videos

Similar Questions

Explore conceptually related problems

((sinx - cosx)/(sinx + cosx))

Show that, sin3x + cos3x = (cosx-sinx)(1+4sinx cosx)

if y=(sinx+cosx)/(sinx-cosx) , then (dy)/(dx) at x=0 is equal to

Evaluate: int(sinx+cosx)/(sinx-cosx)dx

If int(sinx+3cosx)/(sinx+cosx)dx=(kx)/(2)+ln(sinx+cosx) , then k is_________.

int(cosx-sinx)/(1+2sin x cosx)dx is equal to

If P(x)=[(cosx, sinx),(-sinx, cosx)] , then show that P(x).P(y)=P(x+y)=P(y).P(x) .

inte^(x)(sinx+cosx)dx=?

(x+sinx)/(1-cosx)

Prove that (1+sinx-cosx)/(1+sinx+cosx) +(1+sinx+cosx)/(1+sinx-cosx) =2 cosec x