Home
Class 12
MATHS
Evaluate int(cosx-sinx)/(cosx+sinx)(2+2...

Evaluate `int(cosx-sinx)/(cosx+sinx)(2+2sin2x)dx`

A

`sin2x+C`

B

`cos2x+C`

C

`tan2x+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
a
Let `I=int(cosx-sinx)/(cosx+sinx)(2+2sin2x)dx`
`rArrI=2int(cosx-sinx)/(cosx+sinx)xx(cosx+sinx)^(2)dx`
`rArrI=int(cos^(2)x-sin^(2)x)dx=2intcos 2x dx=sin2x+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRALS

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

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|61 Videos

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 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(2cosx-3sinx)/(6cosx+4sinx)dx

Evaluate: int(x-sinx)/(1-cosx)dx

Evaluate int(x+sinx)/(1+cosx)dx

Evaluate: int(x-sinx)/(1-cosx)dx

Evaluate: int(cosx-sinx)/(1+sin2x)\ dx

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

Evaluate: int(1-sinx)/(x+cosx)dx

Evaluate: int(2cosx-sinx)/(2sinx+cosx)\ dx

Evaluate: int(cosx)/(2+3sinx)dx

Evaluate: int(5cosx+6)/(2cosx+sinx+3)dx

OBJECTIVE RD SHARMA ENGLISH-INDEFINITE INTEGRALS-Solved Example
  1. int({x+sqrt(x^(2)+1)})^n/(sqrt(x^(2)+1))dx is equal to

    Text Solution

    |

  2. If int f(x)dx=f(x), then int {f(x)}^(2)dx is equal to

    Text Solution

    |

  3. Evaluate int(cosx-sinx)/(cosx+sinx)(2+2sin2x)dx

    Text Solution

    |

  4. intdx/((2x-7)sqrt(x^2-7x+12) is equal to

    Text Solution

    |

  5. The value of int x log x (log x - 1) dx is equal to

    Text Solution

    |

  6. int(1+x-x^(-1))e ^(x+x^(-1))dx=

    Text Solution

    |

  7. If I(n)=int("In "x)^(n)dx, " then " I(n)+nI(n-1)=

    Text Solution

    |

  8. The value of int(sin^(2)xcos^(2)x)/((sin^(3)x+cos^(3)x)^(2))dx , is

    Text Solution

    |

  9. The integral int(sec^2x)/((secx+tanx)^(9/2))dx equals (for some arbitr...

    Text Solution

    |

  10. If f(x) = int ((x^(2) + sin ^(2)x))/(1+x^(2))sec^(2) x dx and f(0) = ...

    Text Solution

    |

  11. At present, a firm is manufacturing 2000 items. It is estimated tha...

    Text Solution

    |

  12. "If " int f(x)dx=Psi(x), " then " int x^(5)f(x)^(3)dx " is equal to "

    Text Solution

    |

  13. "The integral " int(1+x-(1)/(x))e^(x+(1)/(x))dx " is equal to "

    Text Solution

    |

  14. if int(1-5sin^2x)/(cos^5xsin^2x)dx=f(x)/(cos^5x)+c then f(x)

    Text Solution

    |

  15. int(x^(7m)+x^(2m)+x^m)(2x^(6m)+7x^m+14)^(1/m)dx

    Text Solution

    |

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

    Text Solution

    |

  17. intsqrt(x-3)(sin^(-1)(Inx)+cos^(-1)(Inx))dx is equal to

    Text Solution

    |

  18. "The integral " int(1+x-(1)/(x))e^(x+(1)/(x))dx " is equal to "

    Text Solution

    |

  19. inte^(x^(4))(x+x^(3)+2x^(5))e^(x^(2))dx is equal to

    Text Solution

    |

  20. int(sin(101x).sin^(99)x)dx equals

    Text Solution

    |