Why is reduction formula of $\int \cos^n (x) dx$ restricted to n>1?

Asked Apr 14 '18 at 18:37

Active Apr 14 '18 at 18:37

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$$\int\cos^n x \ dx = \frac{1}n \cos^{n-1}x \sin x + \frac{n-1}{n}\int\cos^{n-2} x \ dx$$

is valid for n>1

The derivation of the reduction formula is well-discussed on the forum e.g, but I can't find anywhere explaining why it is only valid for n>1. Can someone explain?

asked Apr 14 '18 at 18:37

Adroit

Are you sure it's $n>1$, not $n>0$? – Andrew Li Apr 14 '18 at 18:41
That is valid for $n=1$, just not very interesting. – Angina Seng Apr 14 '18 at 19:02
interesting... My problem sheet did say n>1, but i got it to work for n=1. I understand why it does not work for n=0 and below, thanks guys – Adroit Apr 14 '18 at 19:13
1

$n=0$? Thou shalt not divide by zero! – Angina Seng Apr 14 '18 at 19:29

Why is reduction formula of $\int \cos^n (x) dx$ restricted to n>1?

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