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Evaluate the following Integrals : i...

Evaluate the following Integrals :
`int (sec x .dx)/(sqrt(sin (x+2A)+sin A))`

A

`sqrt(secalpha(tanx+tanalpha))+C`

B

`sqrt(2 secalpha(tanx-tanalpha))+C`

C

`sqrt(2 secalpha(tanalpha-tanalpha))+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
a
Let `I=int(secx)/(sqrt(2x+alpha+sinalpha))dx`
`rArr I=int(secx)/(sqrt(2 sin(x+alpha)cosx))dx`
`rArrI=(1)/(sqrt(2))int(sec^(2)x)/(sqrt(tanx cos alpha+sinalpha))dx`
`rArrI=(1)/(sqrt(2)cosalpha)int(1)/(sqrt(tanx cosalpha+sinalpha))d(tanx cosalpha+sinalpha)`
`rArrI=(1)/(sqrt(2)cos alpha)xx2sqrt(tan x cosalpha+sinalpha)+C`
`rArr I=sqrt(2sec^(2)alpha(tan xcosalpha+sinalpha))+C`
`rArrI=sqrt(2secalpha(tanx+tanalpha))+C`.
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  11. Let g (x) be a differentiable function satisfying (d)/(dx){g(x)}=g(x)...

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  12. If intg(x)dx=g(x), then the value of the integral intf(x)g(x){f(x)+2...

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  13. If int (dx)/(1- sin ^(4)x )= a tan x +b tan ^(-1) (c tan x )+ D, then...

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  14. intsin2xlog(e)cosx dx is equal to

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  15. Let f(x) be a polynomial of degree three f(0) = -1 and f(1) = 0. Also,...

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  16. int(1)/(x(1+root(3)(x))^(2))dxis equal to

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  17. Let f(x)=int(x^(2)dx)/((1+x^(2))(1+sqrt(1+x^(2))))and f(0)=0. f(x) i...

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  18. Let f(x) be a polynomial satisfying f(0)=2 , f'(0)=3 and f''(x)=f(x) t...

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  19. int (dx)/((x+1)(x-2))=A log (x+1)+B log (x-2)+C, where

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  20. int(x^(4)+1)/(x^(6)+1)dx is equal to

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