Home
Class 12
MATHS
निम्नलिखित को ज्ञात करे [ Evalute the fo...

निम्नलिखित को ज्ञात करे [ Evalute the following ] :
(i) ` int _(0)^(a) (sqrt(x))/(sqrt(x)+sqrt(a-x))dx `

लिखित उत्तर

Verified by Experts

माना कि ` I = int _(0)^(a) (sqrt(a))/(sqrt(x)+sqrt(a-x))dx" "` (i)
समाकल्य में x कि जगह `(a-x )` रखने पर हमे मिलता है ,
` I = int_(0)^(a)(sqrt(a-x))/(sqrt(a-x)+sqrt(a-(a-x)))dx`
` I = int _(0)^(a) (sqrt(a-x))/(sqrt(a-x)+sqrt(x))dx" " ` …(2)
(1) और (2) को जोड़ने पर हमे मिलता है ,
` 2I = int _(0)^(a) (sqrt(x)+sqrt(a-x))/(sqrt(x)+sqrt(a-x)) dx = int _(0)^(a) 1 dx = [ x ] _(0)^(a) = a - 0 = a`
` :. I = 1/2 a `
Promotional Banner

टॉपर्स ने हल किए ये सवाल

  • निश्चित समाकलों के गुणधर्म

    KC SINHA|Exercise अभ्यास 21.1|65 Videos

  • निश्चित समाकलों के गुणधर्म

    KC SINHA|Exercise अभ्यास 21.2|26 Videos

  • द्वितीय कोटि का अवकलज

    KC SINHA|Exercise OBJECTIVE QUESTIONS|5 Videos

  • प्रतिलोम त्रिकोणमितीय फलन

    KC SINHA|Exercise अभ्यास 4.1|76 Videos
KC SINHA-निश्चित समाकलों के गुणधर्म -OBJECTIVE QUESTIONS
  1. निम्नलिखित को ज्ञात करे [ Evalute the following ] : (i) int (0)^(a...

    Text Solution

    |

  2. int (0)^(pi) cos^(2m+1)" x " dx , where m is a positive integar is eq...

    Text Solution

    |

  3. The value of int (0)^(pi//2) (sqrt(cot x ))/(sqrt(tan x) + sqrt(cot ...

    Text Solution

    |

  4. int (a)^(2a) f(x) dx = 2 int (0)^(a) f(x) dx if

    Text Solution

    |

  5. यदिg(x) = int (0)^(x) cos4tdt फिरg(x + pi) बराबर होगा

    Text Solution

    |

  6. Let f(x) = x - [x] , for every real number x, where [ x] is the integr...

    Text Solution

    |

  7. int (-pi)^(pi) (cos^(2)x)/(1+a^(x)) dx, a gt 0

    Text Solution

    |

  8. Let f, R to R and g : R to R be continous functions . Then the value...

    Text Solution

    |

  9. The value of int (-1)^(2) (|x|)/x dx is

    Text Solution

    |

  10. int (0)^(pi) sqrt((1+cos 2 x)/2) dx is

    Text Solution

    |

  11. For any integar n, the integral int (0)^(pi) e^(sin ^(2)x) . cos^(3)...

    Text Solution

    |

  12. ज्ञात करे । int (pi//4)^(3pi//4) (phi)/(1+sin phi) d phi =

    Text Solution

    |

  13. निम्नलिखित समाकलन का मान निकाले int (0)^(pi//2) (dx)/(1+tan^(3) x )

    Text Solution

    |

  14. int (-1//2)^(1//2) cos x log ((1+x)/(1-x)) dx =

    Text Solution

    |

  15. The value of the integral int (0)^(pi//2) | cos x - sin x | dx is

    Text Solution

    |

  16. int (0)^(2) | x-1| dx is equal to

    Text Solution

    |

  17. The value of the integral int (0)^(pi//2) (sqrt(cos x))/(sqrt(cosx)+ ...

    Text Solution

    |

  18. The value of int (-pi//2)^(pi//2) sqrt((1-cos 2theta )/2 ) d theta ...

    Text Solution

    |

  19. int (-pi//2)^(pi//2) sin^(2) x cos^(2) x ( sin x + cos x ) dx =

    Text Solution

    |

  20. int (-1)^(1) | 1- x| dx =

    Text Solution

    |

  21. int (0)^(pi//2) 1/(1+tan theta ) d theta =

    Text Solution

    |