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Calculus Level 4

Let f : [ 1 , 10 ] → Q f:[1 , 10] \rightarrow \mathbb{Q} be a continuous function.

Find 81 49 ∫ f ( 2 ) f ( 7 ) f ( x ) f ( x ) + f ( 9 − x ) d x \displaystyle \frac{81}{49} \int_{f(2)}^{f(7)} \frac{f(x)}{f(x)+f(9-x)} \ dx .


The answer is 0.000.

Aniket Verma by Aniket Verma , 24, India

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2 solutions

Priyesh Pandey
Apr 12, 2015

This is since f(x) is a constant function . Reason :- the range of f is rational numbers and the function is continuous this could only be possible if f is a constant function => a=0 as f(7)=f(2)=const.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Ya you got it right buddy... (:

Aniket Verma - 6 years, 2 months ago
Hafiz Khan
Apr 11, 2015

b coz f(2)=f(7)

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