Home
Class 12
MATHS
Prove that int0^x e^(x t-t^2) dt=e^(x^(2...

Prove that `int_0^x e^(x t-t^2)` `dt=e^(x^(2)/4)int_0^x e^-(t^(2)/4)dt`

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

y=f(x) satisfies the relation int_(2)^(x)f(t)dt=(x^(2))/2+int_(x)^(2)t^(2)f(t)dt The range of y=f(x) is (a) [0,∞) (b) R (c) (−∞,0] (d) [−1/2,1/2]

y=f(x) satisfies the relation int_(2)^(x)f(t)dt=(x^(2))/2+int_(x)^(2)t^(2)f(t)dt The value of int_(-2)^(2)f(x)dx is

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

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=

A minimum value of the function f(x) = int_(0)^(x) te^(-t^(2))dt is-

Let f:RtoR be a differntiable function satisfying f(x)=x^(2)+3int_(0)^(x^(1/3))e^(-t^(3)).f(x-t^(3))dt . Then find f'(x) .

The option(s) with the values of a and L that satisfy the following equation is (are) (int_0^(4pi)e^t(sin^6at+cos^4at)dt)/(int_0^pi e^t(sin^6at+cos^4at)dt)=L

Let f:R to R be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt . f(x) increases for

Let f:RtoR be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt . y=f(x) is

Let f(x) be a continuous function AAx in R , except at x=0, such that int_0^a f(x)dx , ain R^+ exists. If g(x)=int_x^a(f(t))/t dt , prove that int_0^af(x)dx=int_0^ag(x)dx

CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Show that : pi/6leint0^1dx/sqrt(4-x^2-x^3)lepi/(4sqrt2)

    Text Solution

    |

  2. Let f:[-1,2]->[0,oo) be a continuous function such that f(x)=f(1-x)fo...

    Text Solution

    |

  3. Prove that int0^x e^(x t-t^2) dt=e^(x^(2)/4)int0^x e^-(t^(2)/4)dt

    Text Solution

    |

  4. If alpha=int0^1(e^(9x+3tan^-1x))((12+9x^2)/(1+x^2))dx where tan^-1x t...

    Text Solution

    |

  5. Evaluate int(-4)^(-5)e^((x+5)^(2))dx+3int(1//3)^(2//3)e^(9(x-2/3)^(2))...

    Text Solution

    |

  6. Prove that for any positive integer k ,(sin2k x)/(sinx)=2[cosx+cos3x+...

    Text Solution

    |

  7. Compute the integrals: int0^oof(x^n+x^(-n))logx(dx)/x

    Text Solution

    |

  8. If for a real number y ,[y] is the greatest integral function less, th...

    Text Solution

    |

  9. Compute the integrals: int0^oof(x^n+x^(-n))logx(dx)/(1+x^2)

    Text Solution

    |

  10. If int0^x {int0^u f(t) dt}du is equal to (a) int0^x (x-u) f(u) (b) ...

    Text Solution

    |

  11. Compute the integrals: int(1/e)^e1/xsin(x-1/x)dx

    Text Solution

    |

  12. STATEMENT 1: int0^pixsinxcos^2xdx=pi/2int0^pisinxcos^2x dx. STATEMEN...

    Text Solution

    |

  13. Evaluate: int0^(pi/2)xcosx dx

    Text Solution

    |

  14. Evaluate: int0^(pi/4)(sinx+cosx)/(9+16sin2x)dx

    Text Solution

    |

  15. Evaluate: int(-pi//4)^(pi//4)log(sinx+cosx)dx

    Text Solution

    |

  16. If alpha,beta(beta>alpha), are the roots of g(x)=a x^2+b x+c=0 and f...

    Text Solution

    |

  17. Consider the function f(x) satisfying the relation f(x+1)+f(x+7)=0AAx ...

    Text Solution

    |

  18. Let f: RvecR be a differentiable function having f(2)=6,f^(prime)(2)=1...

    Text Solution

    |

  19. Ifint(sinx)^1t^2f(t)dt=1-sinx ,w h e r e .x in (0,pi/2), then find th...

    Text Solution

    |

  20. Prove that inta^bf(x)dx=int(a+c)^(b+c)f(x-c)dx , and when f(x) is odd ...

    Text Solution

    |