analysis-II-evaluate-1-10-x-2-d-x-x-fractional-part-of-x-

Question Number 131852 by mnjuly1970 last updated on 09/Feb/21

\dots a n a l y s i s (I I) \dots

e v a l u a t e ::

\emptyset = \int_{1}^{10} x^{2} d ({x}) = ?

{x} :: f r a c t i o n a l p a r t o f x \dots

Answered by mr W last updated on 09/Feb/21

ϕ = \int_{1}^{n} x^{2} d ({x})

= \underset{k = 1}{\sum^{n - 1}} \int_{k}^{k + 1} x^{2} d (x - k)

= \underset{k = 1}{\sum^{n - 1}} \int_{k}^{k + 1} x^{2} d x

= \frac{1}{3} \underset{k = 1}{\sum^{n - 1}} [{(k + 1)}^{3} - k^{3}]

= \frac{1}{3} (n^{3} - 1)

f o r n = 10 :

ϕ = 333

Commented by mr W last updated on 09/Feb/21

w h e r e i s t h e m i s t a k e s i r ?

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