Quiz: calculating a definite integral

[Thomas Klemm]

(01-03-2014 06:08 AM)walter b Wrote:  there can be only one correct.

Use integration by parts to get: \(\int_{0}^{1}x^n\log(x)^p dx=-\frac{p}{n+1}\int_{0}^{1}x^n\log(x)^{p-1}dx\)
Iterate starting with \(p=n\) until you end up with: \(\int_{0}^{1}x^n dx=\frac{1}{n+1}\).
You can figure out by yourself which is correct.