Consider a function which is continuous for .
If only attains(or gives output to) rational values in this domain and then find:
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
Before solving this question let us understand one thing. Consider a number line and consider a rational point on it. We know that there are infinite irrational points lying just next to it on its either sides. If we understand this thing then the problem is just a cake walk!
Since the question says that the function f ( x ) only attains rational values and at the same time it is continuous , we can infer that the function is a constant function as even the slightest bend in the curve will mean that it does attain irrational values.
Now since its given that f ( 2 ) = 5 therefore we can conclude that f ( x ) = 5 .
Therefore ∫ − 3 3 f ( x ) d x = 5 [ x ] − 3 3 = 3 0