Home
Class 12
MATHS
If the function f : [0,8] to R is differ...

If the function `f : [0,8] to R` is differentiable, then for `0 < alpha <1 < beta < 2 , int_0^8 f(t) dt ` is equal to

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

If the function f:[0,4]->R is differentiable, the show that for a , b , in (0,4),f^2(4) - f^2(0) =8f^(prime)(a)f(b)

Given a function f:[0,4]toR is differentiable ,then prove that for some alpha,beta in (0,2), int_(0)^(4)f(t)dt=2alphaf(alpha^(2))+2betaf(beta^(2)) .

Prove that the function f(x)=|x| is not differentiable there at x=0.

If f : [-5, 5] to R is a differentiable function function and if f'(x) does not vanish anywhere, then prove that f(-5) ne f(5) .

In the interval 0ltxlt2pi , the function f(x)= |sin2x| is not differentiable at

Let f be any continuously differentiable function on [a, b] and twice differentiable on (a, b) such that f(a)=f'(a)=0" and "f(b)=0 . Then-

A function f:R rarr R satisfies the equation f(x+y)=f(x)f(y) for all x,y in R , f(x) ne 0 . Suppose that the function is differentiable at x=0 and f'(0)=2. Prove that f'(x)=2f(x).

A function f : R to R satisfies the equation f(x + y) = f(x), f(y) for all x, y in R , f(x) ne 0 . Suppose that the function is differentiable at x = 0 and f' (0) = 2. Find (f'(x))/f(x)

Let f be any continuously differentiable function on [a,b] and twice differentiable on (a,b) such that f(a)=f'(a)=0 . Then

Show that the function f(x)=x|x| is continuous and differentiable at x = 0

CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Let intx^(x+p)f(t)dt be independent of xa n dI1=int0^pf(t)dt ,I2=int(1...

    Text Solution

    |

  2. Evaluate: int3^10[log[x]]dx

    Text Solution

    |

  3. If the function f : [0,8] to R is differentiable, then for 0 < alpha...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |