Home
Class 12
MATHS
If f(x) is positive for all positive val...

If f(x) is positive for all positive values of X and `f'(x)lt0,f"(x)gt0,AA x in R^(+)`, prove that `1/2f(1)+int_(1)^(n)f(x)dx lt sum_(r=1)^(n)f(r) lt int_(1)^(n) f(x)dx+f(1)`.

Promotional Banner

Topper's Solved these Questions

  • AREA OF BOUNDED REGIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|23 Videos

  • AREA OF BOUNDED REGIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Subjective Type Questions)|16 Videos

  • BIONOMIAL THEOREM

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

Similar Questions

Explore conceptually related problems

If int_(0)^(100) f(x)dx=7, then sum_(r=1)^(100)int_(0)^(1)f(r-1+x)dx= _________.

Q. if int_0^100(f(x) dx = a , then sum_(r=1)^100(int_0^1( f(r-1+x)dx)) =

int_n^(n+1)f(x) dx=n^2+n then int_(-1)^1 f(x) dx =

If f(x+f(y))=f(x)+yAAx ,y in R and f(0)=1, then prove that int_0^2f(2-x)dx=2int_0^1f(x)dx .

If f(x) is continuous for all real values of x , then sum_(r=1)^nint_0^1f(r-1+x)dx is equal to (a) int_0^nf(x)dx (b) int_0^1f(x)dx (c) int_0^1f(x)dx (d) (n-1)int_0^1f(x)dx

If f(x) is continuous for all real values of x , then sum_(r=1)^nint_0^1f(r-1+x)dx is equal to (a) int_0^nf(x)dx (b) int_0^1f(x)dx (c) int_0^1f(x)dx (d) (n-1)int_0^1f(x)dx

lf f'(x) > 0,f"(x)>0AA x in (0,1) and f(0)=0,f(1)=1 ,then prove that f(x)f^-1(x) lt x^2AA x in (0,1)

If f(x+y)=f(x).f(y) and f(1)=4 .Find sum_(r=1)^n f(r)

Let g(x)gt0andf'(x)lt0,AAx in R, then show g(f(x+1))ltg(f(x-1)) f(g(x+1))ltf(g(x-1))

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in R . If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to

ARIHANT MATHS ENGLISH-AREA OF BOUNDED REGIONS-Area of bounded Regions Exercise 7: Subjective Type Questions
  1. If f(x) is positive for all positive values of X and f'(x)lt0,f"(x)gt0...

    Text Solution

    |