Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: Rs.

There are no items in this cart.
Continue Shopping
Ram Jee Grade:


  Can someone help me solve this question. I wrote IIT JEE2001 and passed. But I am unable to solve this question now :(. I was trying out questions for nostalgic reasons.



Let f(x), x > 0, be a non-negative continuous function, and

let F(x) = ∫0x f(t) dt, x > 0. If for some c > 0, f(x) < cF(x) for all x > 0,

then show that f(x) = 0 for all x > 0.

7 years ago

Answers : (1)

AJIT AskiitiansExpert-IITD
68 Points

Dear Ram ,

visualise it in terms of graphs. f(x) is nonnegative continuous function means graph will be on or above the x-axis. now , F(x) is just area under the curve upto the point x.  so , F(x) >= f(x) as area is always greater than the funciton itself.  i think you have mistyped the relation f(x) < cF(x) ,   f(x) > cF(x) as then actually f(x) = F(x)  = 0   for any c

Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation.

Now you can win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

Win exciting gifts by answering the questions on Discussion Forum

7 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies
  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: Rs. 15,900
  • View Details

Ask Experts

Have any Question? Ask Experts

Post Question

Answer ‘n’ Earn
Attractive Gift
To Win!!! Click Here for details