Home
Class 12
MATHS
If" f, is a continuous function with int...

If" f, is a continuous function with `int_0^x f(t) dt->oo` as `|x|->oo`then show that every line `y = mx` intersects the curve `y^2 + int_0^x f(t) dt = 2`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE ENGLISH|Exercise Jee Advanced (Single|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE ENGLISH|Exercise MATRIX-MATCH TYPE|3 Videos

Similar Questions

Explore conceptually related problems

If f(x)=int_0^x tf(t)dt+2, then

A continuous function f(x) satisfies the relation f(x)=e^x+int_0^1 e^xf(t)dt then f(1)=

If f(-x)+f(x)=0 then int_a^x f(t) dt is

If f is continuous function and F(x)=int_0^x((2t+3)*int_t^2f(u)d u)dt , then |(F''(2))/(f(2))| is equal to_____

Let f be a continuous function on [a , b]dot If F(x)=(int_a^xf(t)dt-int_x^bf(t)dt)(2x-(a+b)), then prove that there exist some c in (a , b) such that int_a^cf(t)dt-int_c^bf(t)dt=f(c)(a+b-2c)dot

If f is continuous function and F(x)=int_0^x((2t+3). int_t^2 f(u)du)\ dt , then |(F^(2))/(f(2))| is equal to____ .

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

Let function F be defined as f(x)= int_1^x e^t/t dt x > 0 then the value of the integral int_1^1 e^t/(t+a) dt where a > 0 is

A function f, continuous on the positive real axis, has the property that for all choices of x gt 0 and y gt 0, the integral int_(x)^(xy)f(t)dt is independent of x (and therefore depends only on y). If f(2) = 2, then int_(1)^(e)f(t)dt is equal to

If int_0^xf(t) dt=x+int_x^1 tf(t)dt, then the value of f(1)

CENGAGE ENGLISH-INTEGRALS-All Questions
  1. For x >0,l e tf(x)=int1^x(logt)/(1+t)dtdot Find the function f(x)+f(1/...

    Text Solution

    |

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

    Text Solution

    |

  3. If" f, is a continuous function with int0^x f(t) dt->oo as |x|->ooth...

    Text Solution

    |

  4. Prove that pi/6 lt int0^1(dx) (sqrt(4-x^2-x^3)) lt pi/(4sqrt(2))

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. int0^x{int0^uf(t)dx}\ du is equal to (a) int0^x(x-u)f(u)du (b) int0...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |