Limits + Integration + Summation!

Calculus Level 5

We denote the two functions f ( x ) = ⌊ x ⌋ − x f(x) = \lfloor x \rfloor - x and g ( x ) = lim ⁡ n → ∞ ( f ( x ) ) 4 n − 1 ( f ( x ) ) 4 n + 1 \displaystyle g(x) = \lim_{n\to\infty} \frac{(f(x))^{4n}-1}{(f(x))^{4n}+1} .

Find the value of ∫ ∑ r = 1 2014 ( g ( x ) ) r d x \displaystyle \int \sum_{r=1}^{2014} (g(x))^r \, dx .

2014 2015 None of These 0

Nishant Rai by Nishant Rai , 25, India

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1 solution

Shuvam Keshari
Sep 25, 2015

g(x)=-1

and the summation=0

now let h(x) be a function such that h(x)=0 for all x.

hence integral of h(x)dx =an arbitrary constant!!

3 Helpful 0 Interesting 0 Brilliant 0 Confused

good\\\\\ trying to trick with indefinite integration

Gaurav Chahar - 5 years, 1 month ago

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