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 Jun 9 revised Curve of intersection of two surfaces added 2208 characters in body Jun 6 asked Curve of intersection of two surfaces Apr 12 asked Integral of $x^{12}(1-x)^8$ Jan 5 awarded Yearling Oct 2 awarded Popular Question Sep 19 awarded Popular Question Jul 29 asked Transform square region to triangular region Jul 2 awarded Curious Jun 20 comment Existence of kth moment I finally figured out your answer, another great answer, but you are right, a huge overestimate. Here is some Mathematica code comparing the actual integral and your bound for $k=6$. In[3]:= k = 6 Out[3]= 6 In[7]:= Integrate[ Abs[x]^k*Exp[-(x - 3)^2], {x, -[Infinity], [Infinity]}] // N Out[7]= 2551.67 In[8]:= Integrate[Abs[x + 3]^k, {x, -1, 1}] + 2^(2*k + 1)*(k + 1)^k // N Out[8]= 9.63783*10^8 Jun 19 awarded Informed Jun 19 asked $E[U^2]=0$ implies $Pr(U=0)=1$ Jun 19 comment Existence of kth moment $|-2|>1$, but $|-2+3|$ is not less than $4(-2)$. Jun 19 comment Existence of kth moment And that's only to the right of $x=1$. Jun 19 comment Existence of kth moment Not sure why the second integral is finite. Here is what I got in Mathematica with $k=20$. Integrate[Abs[x + 3]^k*(k + 1)^(k + 1)/x^(2 (k + 2)), {x, 1, [Infinity]}] // N 1.69501*10^38 Jun 19 comment \$X