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Real Analysis:
Solution
Given that integral a to b f dj exists
As x belongs to [a,b] integral a to x definitely exists for f.
If A'(x) = f(x) then by fundamental theorem of Calculus
A(x) = integral a to x of f dj, where x is in [a,b]
For every point x in [a,b]
lt A(x) exists and equal to A(x) as f is continuous.
Hence A is also continuous.

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Real AnalysisSolutionGiven that integral a to b f dj exists.pdf

  • 1. Real Analysis: Solution Given that integral a to b f dj exists As x belongs to [a,b] integral a to x definitely exists for f. If A'(x) = f(x) then by fundamental theorem of Calculus A(x) = integral a to x of f dj, where x is in [a,b] For every point x in [a,b] lt A(x) exists and equal to A(x) as f is continuous. Hence A is also continuous.