Home
Class 12
MATHS
Let f be a one-to-one continuous functio...

Let `f` be a one-to-one continuous function such that `f(2)=3` and `f(5)=7`. Given `int_2^5 f(x)dx=17,` then find the value of `int_3^7 f^(-1)(x) dx`.

Text Solution

Verified by Experts

The correct Answer is:
`12`
Let `y=f(x)`
`:.x=f^(-1)` and `dy=f'(x)dx`
`I=int_(3)^(7)f^(-1)(x)dx=int_(3)^(7)f^(-1)(y)dy`
Given `f^(-1)(3)=2` and `f^(-1)(7)=5`
`:. I=int_(2)^(5)xf'(x)dx=[x(f(x))]_(2)^(5)-int_(2)^(5)f(x)dx`
`=(5)(7)-(2)(3)-17=12`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise SCQ_TYPE|113 Videos

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise MCQ_TYPE|27 Videos

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise SOLVED EXAMPLE_TYPE|20 Videos

  • CURVE TRACING

    CENGAGE PUBLICATION|Exercise EXERCISES|24 Videos

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

If f(x)=x+sinx , then find the value of int_pi^(2pi)f^(-1)(x)dx .

A continuous real function f satisfies f(2x)=3f(x)AAx in RdotIfint_0^1f(x)dx=1, then find the value of int_1^2f(x)dx

Evaluate: int_(-1)^4f(x)dx=4a n dint_2^4(3-f(x))dx=7, then find the value of int_2^(-1)f(x)dxdot

If int_(-1)^4 f(x) dx =4 and int_2^4[3-f(x)]dx=7 then the value of int_(-1)^2 f(x) dx is

Evaluate: int_(-1)^4f(x)dx=4a n dint_2^4(3-f(x))dx=7, then find the value of int_-1^(2)f(x)dxdot

let T le0 be a fixed real number suppose f is continuous function such that for all x in R f(x+T)=F(x) if I=int_0^T f(x)dx then the value of int_3^(3+3T)f(2x)dx is

If f(0)=1,f(2)=3,f^'(2)=5 ,then find the value of int_0^1xf^('')(2x)dx

Let f: R → R be a one-one onto differentiable function, such that f(2)=1 and f^(prime)(2)=3. Then, find the value of (d/(dx)(f^(-1)(x)))_(x=1)

Let f(x) be a differentiable function such that f(x)=x^2 +int_0^x e^-t f(x-t) dt then int_0^1 f(x) dx=

If f(-x)=-f(x) , then the value of int_(-a)^af(x)dx is equal to

CENGAGE PUBLICATION-DEFINITE INTEGRATION -CAE_TYPE
  1. Show that : int0^1(logx)/((1+x))dx=-int0^1(log(1+x))/x dx

    Text Solution

    |

  2. If int0^1(e^t)/(1+t)dt=a , then find the value of int0^1(e^t)/((1+t)^2...

    Text Solution

    |

  3. Let f be a one-to-one continuous function such that f(2)=3 and f(5)=7....

    Text Solution

    |

  4. Evaluate: ("lim")(n rarr oo)(1/(sqrt(4n^2-1))+1/(sqrt(4n^2-2^2))+ .......

    Text Solution

    |

  5. Evaluate: underset(nrarrinfty)lim[(1/n^2sec^2(1/(n^2))+2/n^2sec^2((4)/...

    Text Solution

    |

  6. Evaluate ("lim")(n rarr oo)sum(k=1)^nk/(n^2+k^2)

    Text Solution

    |

  7. Evaluate the following limit: lim(nto oo)(sum(r=1)^(n) sqrt(r)sum(r=...

    Text Solution

    |

  8. Evaluate the following limit: lim(nto oo)[(n!)/(n^(n))]^(1//n)

    Text Solution

    |

  9. Prove that 4 lt= int1^3 sqrt(3+x^2) dx lt= 4sqrt(3)

    Text Solution

    |

  10. If I1=int0^1 2^(x^2)dx , I2=int0^1 2^(x^3) dx , I3= int1^2 2^(x^2) dx ...

    Text Solution

    |

  11. If II=int0^(pi//2)cos(sinx)dx ,I2=int0^(pi/2)sin(cosx)dx \ ,a n d \ I3...

    Text Solution

    |

  12. Show that : pi/6leint0^1dx/sqrt(4-x^2-x^3)lepi/(4sqrt2)

    Text Solution

    |

  13. Evaluate int(0)^(pi//2)|sinx-cosx|dx.

    Text Solution

    |

  14. Evaluate: int(-1)^4f(x)dx=4a n dint2^4(3-f(x))dx=7, then find the val...

    Text Solution

    |

  15. Evaluate int(1)^(5)sqrt((x-2)sqrt(x-1))dx.

    Text Solution

    |

  16. Evaluate: int(-1)^3(tan^(-1)x/(x^2+1)+tan^(-1)(x^2+1)/x)dx

    Text Solution

    |

  17. Evaluate int(1)^(a)x.a^(-[log(a)x])dx,(agt1).Here [.] represents the g...

    Text Solution

    |

  18. Evaluate: int1^(e^6)[(logx)/3]dx ,w h e r e[dot] denotes the greatest...

    Text Solution

    |

  19. Find the value of int(-1)^1[x^2+{x}]dx ,w h e r e[dot]a n d{dot} denot...

    Text Solution

    |

  20. Prove that int0^x[cot^(-1)x]dx ,w h e r e[dot] denotes the greatest in...

    Text Solution

    |