Prove-that-0-1-tcos-npitdt-1-n-1-n-2-pi-2-

Question Number 88170 by Ar Brandon last updated on 08/Apr/20

P r o v e t h a t

\int_{0}^{1} t c o s n π t d t = \frac{{(- 1)}^{n} - 1}{n^{2} π^{2}}

Commented by jagoll last updated on 08/Apr/20

= \frac{t . \sin n π t}{n π} + \frac{\cos n π t}{n^{2} π^{2}}]_{0}^{1}

= \frac{\sin n π}{n π} + \frac{\cos n π}{n^{2} π^{2}} - \frac{1}{n^{2} π^{2}}

= \frac{{(- 1)}^{n} - 1}{n^{2} π^{2}}

Commented by Joel578 last updated on 08/Apr/20

for n \in N

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