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

$$Provethat$$$${\int }_0^{1}tcosn\pi tdt=\frac{{(-1)}^n-1}{n^2{\pi }^2}$$

Commented by jagoll last updated on 08/Apr/20

$$=\frac{\mathrm{t}.\sin \mathrm{n}\pi \mathrm{t}}{\mathrm{n}\pi }+\frac{\cos \mathrm{n}\pi \mathrm{t}}{{\mathrm{n}}^2{\pi }^2}]{}_0^1$$$$=\frac{\sin \mathrm{n}\pi }{\mathrm{n}\pi }+\frac{\cos \mathrm{n}\pi }{{\mathrm{n}}^2{\pi }^2}-\frac{1}{{\mathrm{n}}^2{\pi }^2}$$$$=\frac{{(-1)}^{\mathrm{n}}-1}{{\mathrm{n}}^2{\pi }^2}$$

Commented by Joel578 last updated on 08/Apr/20

$$\mathrm{for}n\in \mathbb{N}$$

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