Home
Class 11
PHYSICS
Evaluate intsqrt(1+y^(2)).2ydy...

Evaluate `intsqrt(1+y^(2)).2ydy`

Text Solution

Verified by Experts

`"Let"I=intsqrt(1+y^(2)).2ydy`
`"Let" u =1+y^(2)` , then du =2ydy.
`I=int u^(1//2) du`
`=(u^((1//2)+1))/((1//2)+1)` [Integrate , using rule no. 3 with n=1/2]
=`(2)/(3)u^(3//2) +C` [Simpler form]
`=(2)/(3)(1+y^(2))^(3//2)+C` [Replace u by `1+y^(2)`]
Promotional Banner

Topper's Solved these Questions

  • BASIC MATHEMATICS

    GRB PUBLICATION|Exercise Problems For Practice|35 Videos
  • FORCE AND NEWTONS LAWS OF MOTION

    GRB PUBLICATION|Exercise Comprehension|12 Videos

Similar Questions

Explore conceptually related problems

Evaluate: intsqrt (1-x^2)dx

Evaluate: intsqrt (1+x^2)dx

Evaluate intsqrt(x^(2)+2)=p

Evaluate intsqrt(x^(2)+3x)dx .

intsqrt(1+x^(2)/9)dx

Evaluate : (i) intsqrt(9-x^(2))dx (ii) intsqrt(1-4x^(2))dx (iii) intsqrt(16-9x^(2))dx

Evaluate : (i) intsqrt(x^(2)-16)dx (ii) intsqrt(4x^(2)-5)dx (iii) intsqrt(17x^(2)-11)dx

Evaluate intsqrt(1+3x-x^2)dx .

Evaluate intsqrt (4-x^2)dx

Evaluate : intsqrt(4-x-x^(2))dx .

GRB PUBLICATION-BASIC MATHEMATICS-Problems For Practice
  1. If y=cos^(2) x, then find (dy)/(dx).

    Text Solution

    |

  2. If y=cos x^(2), then find (dy)/(dx) .

    Text Solution

    |

  3. If x=at^(4), y=bt^(3), then find (dy)/(dx).

    Text Solution

    |

  4. The velocity v of a particle is given by the equation v=6t^(2)-6t^(3)...

    Text Solution

    |

  5. Evaluate intsqrt(1+y^(2)).2ydy

    Text Solution

    |

  6. Evaluate : int (2xdx)/((x^(2)+1)^(3//2)

    Text Solution

    |

  7. How rapidly will the fluid level inside a vertical cylindrical tank dr...

    Text Solution

    |

  8. A hot air balloon rising straight up from a level field is tracked by...

    Text Solution

    |

  9. A police cruiser, approaching a right-angled intersection from the nor...

    Text Solution

    |

  10. Water runs into a conical tank at the rate of 9 ft^(3)//"min". The ta...

    Text Solution

    |

  11. Heating a plate. When a circular plate of metal is heated in an oven, ...

    Text Solution

    |

  12. Changing dimensions in a rectangular box. Suppose that the edge lengt...

    Text Solution

    |

  13. A 13 ft leader is leaning against a house when its base starts to sli...

    Text Solution

    |

  14. Flying a kite . A girl flies a kite at a height of 3000 ft, the wind ...

    Text Solution

    |

  15. A growing sand pile . Sand falls from a conveyor belt at the rate of ...

    Text Solution

    |

  16. A growing raindrop. Suppose that a drop of mist is a perfect sphere an...

    Text Solution

    |

  17. A balloon and a bicycle. A balloon is rising vertically above a level...

    Text Solution

    |

  18. If two resistors of R(1) and R(2) ohms are connected in parallel in an...

    Text Solution

    |

  19. Suppose that at time t ul( gt)0 the position of a particle moving on ...

    Text Solution

    |

  20. A draining conical reservoir. Water is flowing at the rate of 50m^(3)/...

    Text Solution

    |