E-PI04 · A finite integral with a tail
For \(b\ge1\), let \(\displaystyle I(b)=\int_1^b\frac6{x^4}\,dx\).
Find I(b) explicitly.
Evaluate \(\int_1^\infty6x^{-4}\,dx\). Is this value attained by I(b) for a finite b?
Find the least integer b such that the remaining integral from b to infinity is less than \(\displaystyle \frac1{50}\).
Complete-answer checking, worked solutions and indicative written criteria.
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