Give an example of a function which is not integrable on [0,π].Justify your answer.?
1 Answer
Explanation:
For a function to be non-integrable on a certain interval, we require that function to have a vertical asymptote on that interval. When thinking of the definite integral as the area under the curve, a vertical asymptote within the interval (or at one of the endpoints) stops us from taking the area right away and forces us to split our integral into separate intervals in the case of a discontinuity within the interval.
Think of a function that has a vertical asymptote on the interval
Consider the function
Any other function with a vertical asymptote on
Infinitely many functions could meet this requirement, but