# Understand the problem

Let be a nonnegative continuous function on s.t is finite then

##### Source of the problem

TIFR 2018 Part A, Problem 4

##### Topic

Analysis

##### Difficulty Level

Hard

##### Suggested Book

Real Analysis; Bartle and Sherbert

# Start with hints

Do you really need a hint? Try it first!

Can you think of a function such that it has finite area but as goes to infinity, goes to infinity?

Try to sketch the above function. Picture

See if the exists then it must be zero right? but what if the limit fails to exist and the integral still gives you finite value? Hence, this is the case drawn in the above picture. Hence the answer is false generally.

# Watch the video

# Connected Program at Cheenta

#### College Mathematics Program

The higher mathematics program caters to advanced college and university students. It is useful for I.S.I. M.Math Entrance, GRE Math Subject Test, TIFR Ph.D. Entrance, I.I.T. JAM. The program is problem driven. We work with candidates who have a deep love for mathematics. This program is also useful for adults continuing who wish to rediscover the world of mathematics.