Math Question and Answers


Question and Answers Forum

All Questions Topic List
Integration Questions
Previous in All Question Next in All Question
Previous in Integration Next in Integration
Question Number 51910 by Meritguide1234 last updated on 01/Jan/19

Commented by Abdo msup. last updated on 01/Jan/19

$l e t f i n d {f i r s t I}_{n} = \int_{0}^{π} {c o s}^{n} x c o s (n x) d x w i t h n f r o m N$ $I_{n} = R e (\int_{0}^{π} {c o s}^{n} x e^{i n x} d x) a n d$ $\int_{0}^{π} {c o s}^{n} x e^{i n x} d x = \int_{0}^{π} {(\frac{e^{i x} + e^{- i x}}{2})}^{n} e^{i n x} d x$ $= \frac{1}{2^{n}} \int_{0}^{π} (\sum_{k = 0}^{n} C_{n}^{k} e^{i k x} (e^{- i (n - k) x}) e^{i n x} d x$ $= \frac{1}{2^{n}} \int_{0}^{π} (\sum_{k = 0}^{n} C_{n}^{k} e^{i 2 k x}) d x$ $= \frac{1}{2^{n}} \sum_{k = 0}^{n} \int_{0}^{π} e^{2 i k x} d x = \frac{1}{2^{n}} (π + \sum_{k = 1}^{n} {[\frac{1}{2 i k} e^{2 i k x}]}_{0}^{π})$ $= \frac{π}{2^{n}} \Rightarrow \frac{π}{I_{n}} = 2^{n} \Rightarrow {l o g}_{2} (\frac{π}{I_{n}}) = n \Rightarrow$ ${l o g}_{2} (\frac{π}{\int_{0}^{π} {c o s}^{2019} x c o s (2019) x d x}) = 2019 .$
Commented by tanmay.chaudhury50@gmail.com last updated on 01/Jan/19

$e x c l l e n t . . .$
Commented by Meritguide1234 last updated on 01/Jan/19

$g o o d$
Commented by maxmathsup by imad last updated on 01/Jan/19

$t h a n k s . . .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum