Home
Class 12
MATHS
Evaluate the definite integralsint0^(pi...

Evaluate the definite integrals`int_0^(pi/2)(cos^2x dx)/(cos^2x+4sin^2x)`

Text Solution

Verified by Experts

Given `int_0^(pi/2)(cos^2x dx)/(cos^2x+4sin^2x)`
Divide numerator an denominator by `cos^4x`
`I=int_0^(pi/2) (sec^2x)/(sec^2x+4tan^2xsec^2x) dx`
`=int_0^(pi/2) (sec^2x)/(sec^2x(1+4tan^2x) dx`
...
Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    NCERT|Exercise EXERCISE 7.3|24 Videos

  • INTEGRALS

    NCERT|Exercise SOLVED EXAMPLES|46 Videos

  • INTEGRALS

    NCERT|Exercise EXERCISE 7.5|23 Videos

  • DIFFERENTIAL EQUATIONS

    NCERT|Exercise EXERCISE 9.1|12 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    NCERT|Exercise MISCELLANEOUS EXERCISE|17 Videos

Similar Questions

Explore conceptually related problems

Evaluate the following integral: int_0^(pi//2)x^2cos2x\ dx

Evaluate: int_0^(pi//2)(cos^2x)/(cos^2x+4sin^2x)dx

Evaluate the definite integrals int_(0)^((pi)/(4))(sin x cos x)/(cos^(4)x+sin^(2)x)dx

Evaluate the following integral: int_0^(pi//2)(cos x)/(1+sin^2x)dx

Evaluate the following integral: int_0^(pi//2)(cos x)/(1+sin^2x)dx

Find the Definite Integrals : int_0^(pi/2) sin^2x cos^3x dx

Evaluate the definite integrals int_(0)^( pi)((sin^(2)x)/(2)-(cos^(2)x)/(2))dx

Evaluate the following integral: int_0^(pi//2)(cos^2x)/(1+3sin^2x)dx

Evaluate the definite integrals int_(0)^((pi)/(4))(sin x+cos x)/(9+16sin2x)dx

NCERT-INTEGRALS-MISCELLANEOUS EXERCISE
  1. Evaluate the definite integralsint0^1 (dx)/(sqrt(1+x)-sqrt(x))

    Text Solution

    |

  2. Evaluate the definite integralsint(pi/6)^(pi/3)(sinx+cosx)/(sqrt(sin2...

    Text Solution

    |

  3. Evaluate the definite integralsint0^(pi/2)(cos^2x dx)/(cos^2x+4sin^2x...

    Text Solution

    |

  4. Evaluate the definite integralsint0^(pi/4 ) (sinxcosx)/(cos^4x+sin^4x)...

    Text Solution

    |

  5. Evaluate the definite integrals int(pi/2)^pie^x((1-sinx)/(1-cosx))dx

    Text Solution

    |

  6. Integrate the functions(sqrt(x^2+1)[log(x^2+1)-2logx])/(x^4)

    Text Solution

    |

  7. Integrate the functionstan^(-1)sqrt((1-x)/(1+x))

    Text Solution

    |

  8. Integrate the functions(x^2+x+1)/((x+1)^2(x+2)

    Text Solution

    |

  9. Integrate the functions(2+sin2x)/(1+cos2x)e^x

    Text Solution

    |

  10. Integrate the functionssqrt((1-sqrt(x))/(1+sqrt(x)))

    Text Solution

    |

  11. Evaluate the definite integralsint0^(pi/4)(sinx+cosx)/(9+16sin2x)dx

    Text Solution

    |

  12. Evaluate the definite integralsint0^(pi/2)sin2xtan^(-1)(sinx)dx

    Text Solution

    |

  13. Choose the correct answersint(cos2x)/((sinx+cosx)^2)dxis equal(A) (-1)...

    Text Solution

    |

  14. Evaluate the definite integralsint0^pi (xtanx)/(secx+tanx)dx

    Text Solution

    |

  15. Evaluate the definite integralsint1^4[|x-1|+|x-2|+|x-3|]dx

    Text Solution

    |

  16. Prove thatint1^3(dx)/(x^2(x+1))=2/3+log2/3

    Text Solution

    |

  17. Prove thatint0^1x e^x dx=1

    Text Solution

    |

  18. Prove thatint0^(pi/4) 2tan^3xdx=1-log2

    Text Solution

    |

  19. Prove thatint0^(pi/2)sin^3xdx=2/3

    Text Solution

    |

  20. Integrate the functions(sinx)/(sin(x-a)

    Text Solution

    |