Home
Class 12
MATHS
Integrate the function is Exercise. (s...

Integrate the function is Exercise.
`(sin^(-1) sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1) sqrt(x)+cos^(-1) sqrt(x)), x in [0,1]`

Text Solution

Verified by Experts

The correct Answer is:
`=(2(2x-1))/(pi) sin^(-1)x+ (2sqrt (x-x^(2)))/(2)-c`
Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    KUMAR PRAKASHAN|Exercise TEXTBOOK ILLUSTRATIONS FOR PRACTICE WORK|45 Videos

  • INTEGRALS

    KUMAR PRAKASHAN|Exercise SOLUTIONS OF NCERT EXEMLAR PROBLEMS (Short Answer Type Questions)|33 Videos

  • INTEGRALS

    KUMAR PRAKASHAN|Exercise EXERCISE 7.11|21 Videos

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Practice Paper-4 (Section-D)|2 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER - 2 (SECTION - D)|2 Videos

Similar Questions

Explore conceptually related problems

Integrate the function in Exercise. x sin^(-1)x

Integrate the function in Exercise. x cos^(-1)x

Integrate the function in Exercise. (sin^(-1)x)^(2)

Integrate the function in Exercise. (1)/(x- sqrt(x))

Integrate the function in Exercise. x sqrt(x+2)

Integrate the function in Exercise. sqrt(sin 2x)cos 2x

Integrate the function in Exercise. (cos sqrt(x))/(sqrt(x))

KUMAR PRAKASHAN-INTEGRALS -MISCELLANEOUS EXERCISE-7
  1. Integrate the functions f'(ax+b)[f(ax+b)]^(n)

    Text Solution

    |

  2. Integrate the function is. (1)/(sqrt(sin^(3)x sin(x+alpha)))

    Text Solution

    |

  3. Integrate the function is Exercise. (sin^(-1) sqrt(x)-cos^(-1)sqrt(x...

    Text Solution

    |

  4. Integrate the function is Exercise. sqrt((1-sqrt(x))/(1+sqrt(x)))

    Text Solution

    |

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

    Text Solution

    |

  6. Integrate the function is Exercise. (x^(2)+x+1)/((x+1)^(2)+(x+2))

    Text Solution

    |

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

    Text Solution

    |

  8. Integrate the function is (xcos^-1x)/sqrt(1-x^2)

    Text Solution

    |

  9. Evaluate the definite integrals int(pi/2)^(pi)e^(x)((1-sinx)/(1-cosx...

    Text Solution

    |

  10. Evaluate the definite integrals int(0)^(pi/4)(sinxcosx)/(cos^(4)x+si...

    Text Solution

    |

  11. Evaluate the definite integrals in exercise. overset((pi)/(2)) under...

    Text Solution

    |

  12. Evaluate the definite integrals in exercise. overset((pi)/(3)) under...

    Text Solution

    |

  13. Evaluate the definite integrals int(0)^(1)(dx)/(sqrt(1+x)-sqrtx)

    Text Solution

    |

  14. Evaluate the definite integrals int(0)^(pi/4)(sinx+cosx)/(9+16sin2x)...

    Text Solution

    |

  15. Evaluate the definite integrals int(0)^(pi/2)sin2xtan^(-1)(sinx)dx

    Text Solution

    |

  16. Evaluate the definite integrals int(0)^(pi)(xtanx)/(secx+tanx)dx

    Text Solution

    |

  17. Evaluate the definite integrals int(1)^(4)[abs(x-1)+abs(x-2)+abs(x-3...

    Text Solution

    |

  18. Evaluate the following definite integrals : int(1)^(3)(dx)/(x^(2)(x+...

    Text Solution

    |

  19. Prove the following int(0)^(1)xe^(x)dx=1

    Text Solution

    |

  20. Prove the following int(-1)^(1)x^(17)cos^(4)xdx=0

    Text Solution

    |