Home
Class 12
MATHS
Evaluate: int(sqrt(tanx)+sqrt(cotx))dx...

Evaluate: `int(sqrt(tanx)+sqrt(cotx))dx`

A

` sin^(-1)(sin x-cos c)+C`

B

`sqrt(2)sin ^(-1)(sinx - cosx)+C`

C

`t=sqrt(2)cos^(-1)(sin x-cosx)+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
b
We have, `I=int{sqrt(tanx)+sqrt(cosx)}dx=int(sinx +cos x)/(sqrt(sin x cos x))dx`
`rArr I= sqrt(2)int(sin x +cos x)/(sqrt(2 sin x cosx))dx`
`rArrI= sqrt(2)int(1)/(sqrt(1-(sinx - cos x )^(2)))d(-cos x +sin x)`
`rArr I=sqrt(2)sin ^(-1)(sin x - cos x)+C`.
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Solved Example|92 Videos

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|3 Videos

  • INCREASING AND DECREASING FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|18 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

Evaluate: int(sqrt(tanx))dx

Evaluate : int ( sqrt( tan x) - sqrt( cot x)) dx

Evaluate: int(sec^2sqrt(x))/(sqrt(x))dx

Evaluate: int1/(sqrt(x)(sqrt(x)+1))\ dx

Evaluate: int(sqrt(tanx))/(sinxcosx)dx

Evaluate: int(sqrt(tanx))/(sinxcosx)dx

Evaluate: int1/(sqrt(x)+sqrt(x+1))\ dx

Evaluate: int(dx)/(sqrt(x)+sqrt(x-2))

Evaluate: int(dx)/(sqrt(x)+sqrt(x-2))

Evaluate: int(sqrt(cotx)-sqrt(tanx))/(1+3sin2x)dx

OBJECTIVE RD SHARMA ENGLISH-INDEFINITE INTEGRALS-Chapter Test
  1. Evaluate: int(sqrt(tanx)+sqrt(cotx))dx

    Text Solution

    |

  2. The integral int (2x-3)/(x^2+x+1)^2 .dx is equal to

    Text Solution

    |

  3. If int(xtan^(-1)x)/sqrt(1+x^(2))dx = sqrt(1+x^(2))f(x) + A " ln "sqrt(...

    Text Solution

    |

  4. "If " int xlog(1+1//x)dx=f(x)log(x+1)+g(x)x^(2)+Ax+C, then

    Text Solution

    |

  5. If int(xe^(x))/(sqrt(1+e^(x)))dx=f(x)sqrt(1+e^(x))-2logg(x)+C, then

    Text Solution

    |

  6. The value of int (cos^3x+cos^5)/(sin^2x+sin^4x)dx

    Text Solution

    |

  7. If int(dx)/((x^(2)+1)(x^(2)+4))=k tan^(-1) x + l tan^(-1) . (x)/(2) +C...

    Text Solution

    |

  8. If int log(sqrt(1-x)+sqrt(1+x))dx=xf(x)+Ax+Bsin^(-1)x+C, then

    Text Solution

    |

  9. If int(x^(5))/(sqrt(1+x^(3)))dx is equal to

    Text Solution

    |

  10. The value of : inte^(secx).sec^(3)x(sin^(2)x+cosx+sinx+sinxcosx)dx i...

    Text Solution

    |

  11. If int(2x^(2)+3)/((x^(2)-1)(x^(2)+4))dx=aln((x-1)/(x+1))+btan^(-1).(x)...

    Text Solution

    |

  12. Let f(x)=(x)/((1+x^(n))^(1//n)) for n ge 2 and g(x)=underset("n times"...

    Text Solution

    |

  13. The value of int ((ax^(2)-b)dx)/(xsqrt(c^(2)x^(2)-(ax^(2)+b)^(2))) is ...

    Text Solution

    |

  14. Evalaute: inte^(x)(1+nx^(n-1)-x^(2n))/((1-x^(n))sqrt(1-x^(2n))dx

    Text Solution

    |

  15. int(xcosx+1)/(sqrt(2x^(3)e^(sinx)+x^(2)))dx

    Text Solution

    |

  16. int(x^(3))/((1+x^(2))^(1//3))dx is equal to

    Text Solution

    |

  17. int sinx/sin(x-alpha)dx=Ax+B log (sin(x-alpha))+C then find out (A ,B)

    Text Solution

    |

  18. What is int (x^(2) +1)/(x^(4) - x^(2) + 1) dx equal to ?

    Text Solution

    |

  19. Evaluate: int(x-1)/((x+1)sqrt(x^3+x^2+x))dx

    Text Solution

    |

  20. int(1+x^(2))/(xsqrt(1+x^(4)))dx is equal to

    Text Solution

    |

  21. int(1+x^(4))/((1-x^(4))^(3//2))dx is equal to

    Text Solution

    |