Home
Class 12
MATHS
Let intx^(x+p)f(t)dt be independent of x...

Let `int_x^(x+p)f(t)dt` be independent of `xa n dI_1=int_0^pf(t)dt ,I_2=int_(10)^(p^n+10)f(z)dz` for some `p ,` where `n in Ndot` Then evaluate `(l_2)/(l_1)dot`

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Jee Advanced (Single|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise TRUE OR FALSE|1 Videos

Similar Questions

Explore conceptually related problems

Let int_x^(x+p)f(t)dt be independent of x and I_1=int_0^p f(t) dt , I_2 = int_(10)^(p^n+10) f(z) dz for some p , where n in N . Then evaluate (I_2)/(I_1) .

Let f(x) = int_2^x f(t^2-3t+2) dt then

If f(t) is an odd function, then int_(0)^(x)f(t) dt is -

If int_(0)^(x) f(t)dt=x+int_(x)^(1)t f(t)dt , find the value of f(1).

Find the points of minima for f(x)=int_0^x t(t-1)(t-2)dt

If int_[x]^(x+1) f(t)dt =[x] then th value of int_(-2)^4 f(x) dx is equal

if int_0^(x^2(1+x))f(t)dt=x then the value of 10f(2) must be

If f(x)=x+int_0^1 t(x+t) f(t)dt, then find the value of the definite integral int_0^1 f(x)dx.

If f(x)=int_0^x(sint)/t dt ,x >0, then

If x int_(0)^(x)sin(f(t))dx=(x+2)int_(0)^(1)tsin(f(t))dt , where xgt0 , then show that f'(x)cot f(x)+3/(1+x)=0

CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. If the function f : [0,8] to R is differentiable, then for 0 < alpha...

    Text Solution

    |

  2. The value of int0^1(x^4(1-x)^4)/(1+x^2)dx is/are (a)(22)/7-pi (b)...

    Text Solution

    |

  3. Let intx^(x+p)f(t)dt be independent of xa n dI1=int0^pf(t)dt ,I2=int(1...

    Text Solution

    |

  4. Evaluate:int-pi^pi ((2x)(1+sinx)/(1+cos^2x))dx

    Text Solution

    |

  5. Q. if int0^100(f(x) dx = a, then sum(r=1)^100(int0^1( f(r-1+x)dx))=

    Text Solution

    |

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

    Text Solution

    |

  7. If int0^1 e^(x^2)(x-alpha)dx=0, then (a)alphalt2 (b)alphalt0 (c)"" 0l...

    Text Solution

    |

  8. int(5/2)^5(sqrt((25-x^2)^3))/(x^4)dx is equal to

    Text Solution

    |

  9. The value of int0^((3pi)/2)(|tan^(-1)(tanx)|-|sin^(-1)(sinx)|)/(|tan^(...

    Text Solution

    |

  10. Let f(0)=0a n dint0^2f^(prime)(2t)e^(f(2t))dt=5.t h e nv a l u eoff(4)...

    Text Solution

    |

  11. The value of the integral int0^oo(xlogx)/((1+x^2)^2)dx ,is (a)0 (...

    Text Solution

    |

  12. int0^pi(xtanx)/(secx+cosx)dx is (pi^2)/4 (b) (pi^2)/2 (c) (3pi^2)/2...

    Text Solution

    |

  13. Ifint(log2)^x(dx)/(sqrt(e^x-1))=pi/6,"then " x " is equalto" 4 (b) ...

    Text Solution

    |

  14. The solution for x of the equation int(sqrt(2))^x(dt)/(tsqrt(t^2-1))=p...

    Text Solution

    |

  15. Which of the following is incorrect? int(a+ c)^(b+c)f(x)dx=inta^bf(x...

    Text Solution

    |

  16. The value of the integral int(-pi)^pisinm xsinn xdx , for m!=n(m , n i...

    Text Solution

    |

  17. Evaluate: int(e^x(2-x^2)dx)/((1-x)sqrt(1-x^2))

    Text Solution

    |

  18. int0^oo(pi/(1+pi^2x^2)-1/(1+x^2))logx dx is equal to (a) -pi/2logpi (...

    Text Solution

    |

  19. If f(x)="cos"(tan^(-1)x), then the value of the integral int0^1xf''(x)...

    Text Solution

    |

  20. The equation of the curve is y=f(x)dot The tangents at [1,f(1),[2,f(2)...

    Text Solution

    |