Home
Class 12
MATHS
about to only mathematics...

about to only mathematics

Text Solution

Verified by Experts

The correct Answer is:
6
`y=f(x)impliesx=f^(-1)(y)impliesx=g(y)`
Given `y=f(x)=int_(0)^(x)(dt)/(sqrt(1+t^(3))`
`(dy)/(dx)=1/(sqrt(1+x^(3))` or `(dx)/(dy)=sqrt(1+x^(3))`
`g'(y)=sqrt(1+g^(3)(y))`
`g''(y)=(3g^(2)(y)g'(y))/(2sqrt(1+g^(3)(y)))`
`:. 2g''(y)=3g^(2)(y)(g'(y))/(sqrt(1+g^(3)(y)))=3g^(2)(y)(sqrt(1+g^(3)(y)))/(sqrt(1+g^(3)(y)))=3g^(2)(y)`
or `2g''(y)=3g^(2)(y)`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE|Exercise JEE Main Previous Year|12 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise JEE Advanced Previous Year|38 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Matrix)|6 Videos

  • CURVE TRACING

    CENGAGE|Exercise Exercise|24 Videos

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

A school library has 75 books on Mathematics, 35 books on physics. A student can choose only one book , In how many ways a student can choose a book on Mathematics or physics?

The first theorem in mathematics is ………… .

There are 15 candidates for an examination . 7 candidates are appearing for mathematics examination while the remaining 8 are appearing for different subjects. In how many ways can they be seated in a row so that no two mathematics candidates are together ?

There are 15 candidates for an examination. 7 candidates are appearing for mathematics examination while the remaning 8 are appearing for different subjects. In how many ways can they be seated in a row so that no two mathematics candidates are together?

There are 15 candidates for an examination. 7 candidates are appearing for mathematics examination while the remaining 8 are appearing for different subjects . In how many ways can they be seated in a row so that no two mathematics candidates are together ?

A bag contains a total of 20 books on physics and mathematics, Any possible combination of books is equally likely. Ten books are chosen from the bag and it is found that it contains 6 books of mathematics. Find out the probability that the remaining books in the bag contains 3 books on mathematics.

Formulate into a mathematical problem to find a number such that when its cube root is added to it, the result is 6.

CENGAGE-DEFINITE INTEGRATION -Exercise (Numerical)
  1. The value of int(0)^(1)(tan^(-1)x)/(cot^(-1)(1-x+x^(2))dx is.

    Text Solution

    |

  2. Let f(x) be differentiate function symmetric about x=2, then the value...

    Text Solution

    |

  3. Let f:[0,oo)vecR be a continuous strictly increasing function, such th...

    Text Solution

    |

  4. If f is continuous function and F(x)=int0^x((2t+3)dotintt^2f(u)d u)dt ...

    Text Solution

    |

  5. If the value of the definite integral int0^1(sin^(-1)sqrt(x))/(x^2-x+1...

    Text Solution

    |

  6. about to only mathematics

    Text Solution

    |

  7. Let g(x) be differentiable on R and int(sint)^1x^2g(x)dx=(1-sint), wh...

    Text Solution

    |

  8. If int0^oox^(2n+1)dote^(-xdx)=360 , then the value of n is

    Text Solution

    |

  9. Let f(x) be a derivable function satisfying f(x)=int0^x e^tsin(x-t)dt...

    Text Solution

    |

  10. Let f(x)=1/x^2 int0^x (4t^2-2f'(t))dt then find f'(4)

    Text Solution

    |

  11. If the value of the definite integral int0^1^(2007)C7x^(2000)dot(1-x)^...

    Text Solution

    |

  12. IfIn=int0^1(1-x^5)^n dx ,t h e n(55)/7(I(10))/(I(11))i se q u a lto

    Text Solution

    |

  13. Evaluate: 5050(int0 1(1-x^(50))^(100)dx)/(int0 1(1-x^(50))^(101)dx)

    Text Solution

    |

  14. L e tJ=int(-5)^(-4)(3-x^2)tan(3-x^2)dxa n dK=int(-2)^(-1)(6-6x+x^2) t...

    Text Solution

    |

  15. The value of the definite integral int(2-1)^(sqrt(2)+1)(x^4+x^2+2)/((x...

    Text Solution

    |

  16. Consider a real valued continuous function f such that f(x)=sinx + int...

    Text Solution

    |

  17. Iff(x)=x+int0^1t(x+t)f(t)dt ,t h e nt h ev a l u eof(23)/2f(0) is ...

    Text Solution

    |

  18. Let y=f(x)=4x^(3)+2x-6, then the value of int(0)^(2)f(x)dx+int(0)^(30)...

    Text Solution

    |

  19. The value of int(1)^(3)(sqrt(1+(x-1)^(3))+(x^(2)-1)^(1/3)+1)dx is .

    Text Solution

    |

  20. The value of int(0)^(1)xcos^(-1)((1-x^2)/(1+x^2)) dx (x>0) is equal to...

    Text Solution

    |