Home
Class 12
MATHS
Evaluate (lim)(x to 4)int4^x((4t-f(t)))...

Evaluate `(lim)_(x to 4)int_4^x((4t-f(t)))/((x-4))dt`

Text Solution

Verified by Experts

The correct Answer is:
`16-f(4)`
`L=lim_(xto4)int_(4)^(x)((4t-f(t)))/((x-4))dt=limt_(xto4)(int_(4)^(1)(4t-f(t))dt)/(x-4)`
( `0//0` form , using L Hopital's rule)
`=lim_(xto 4)(4x-f(x))/1`
`16-f(4)`
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

Let f: R->R be a differentiable function having f(2)=6,f^(prime)(2)=1/(48)dot Then evaluate ("lim")_(x->2)int_6^(f(x))(4t^3)/(x-2)dt

Let f:R to R be a differentiable function and f(1)=4 and f'(1)=2 , then the value of lim_(x to 1) int_(4)^(f(x))(2t)/(x-1)dt is -

Let f: RvecR be a differentiable function having f(2)=6,f^(prime)(2)=1/(48)dot Then evaluate lim_(xto2)int_6^(f(x))(4t^3)/(x-2)dt

The value of lim_(xto2)int_(2)^(x)(3t^(2))/(x-2)dt is

The value of lim_( x to 0) (int_(0)^(x^(2)) cos(t^(2))dt)/(x sinx) is

The value of lim_(x to 0)(int_(0)^(x^(2))sec^(2)t dt)/(x sin x) is equal to -

lim_(x rarrpi/4)(int_2^(sec^2x) f(t)dt)/(x^2-pi^2/16)

Newton-Leinbnitz's formula states that d/dx(int_(phi(x))^(psi(x)) f(t)dt)=f(psi(x)){d/dxpsi(x)}-f(phi(x)){d/dxphi(x)} Answer the following questions based on above passage: Let f(x) be a differentiable function and f(1)=2, If lim_(xrarr1)int_2^(f(x)) (2t)/(x-1)dt=4 , then the value of f'(1) is equal to

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

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

CENGAGE PUBLICATION-DEFINITE INTEGRATION -CAE_TYPE
  1. Ifint(pi/3)^xsqrt((3-sin^2t))dt+int0^ycostdt=0,then evaluate (dy)/(d...

    Text Solution

    |

  2. Iff(x)=e^(g(x))a n dg(x)=int2^x(tdt)/(1+t^4), then find the value of ...

    Text Solution

    |

  3. Evaluate (lim)(x to 4)int4^x((4t-f(t)))/((x-4))dt

    Text Solution

    |

  4. Evaluate: lim(xto0)(int(0)^(x^(2))cos^(2)tdt)/(xsinx)

    Text Solution

    |

  5. Find the points of minima for f(x)=int0^x t(t-1)(t-2)dt

    Text Solution

    |

  6. Find the equation of tangent to y=int(x^2)^(x^3)(dt)/(sqrt(1+t^2))a t...

    Text Solution

    |

  7. I f f(x)=int((pi^2)/(16))^(x^2)(sinxsinsqrt(theta))/(1+cos^2sqrt(theta...

    Text Solution

    |

  8. If f(x) is a function satisfying f(x+a)+f(x)=0 for all x in R and pos...

    Text Solution

    |

  9. Let f(x) be a differentiable function satisfying f(x)=int(0)^(x)e^((2t...

    Text Solution

    |

  10. Ifint0^1(e^t dt)/(t+1)=a ,then find the value of int(b-1)^b(e^(-t)dt)/...

    Text Solution

    |

  11. f(x)=int1^xlogt/(1+t+t^2)dt (xge1) then prove that f(x) =f(1/x)

    Text Solution

    |

  12. f(x)=int1^x(tan^(-1)(t))/t dt \ AAx in R^+, then find the value of f...

    Text Solution

    |

  13. Evaluate: int(sqrt(2)-1)^(sqrt(2)+1)((x^2-1))/((x^2+1)^2)dx

    Text Solution

    |

  14. Evaluate: int0^(e-1)((x^2+2x-1)/2)/(x+1)dx+int1^e xlogx e^(x^(2-2)/2)d...

    Text Solution

    |

  15. Find the value of int(1/2)^(2)e^(|x-1/x|)dx.

    Text Solution

    |

  16. If I(1)=int(0)^(1)(dx)/(e^(x)(1+x)) and I(2)=int(0)^(pi//4)(e^(tan^(2)...

    Text Solution

    |

  17. If IK=int1^e(1nx)^kdx(k in I^+)dx(k in I^+), then find the value of ...

    Text Solution

    |

  18. Given Im=int1^e(logx)^mdx ,then prove that(Im)/(1-m)+m I(m-2)=e

    Text Solution

    |

  19. If I(n)=int(0)^(pi)x^(n)sinxdx, then find the value of I(5)+20I(3).

    Text Solution

    |

  20. If L(m,n)=int(0)^(1)t^(m)(1+t)^(n),dt, then prove that L(m,n)=(2^(n)...

    Text Solution

    |