Question

Let xe R. Compute - 1x av R X/ Hint: this is another improper integral, but this time in three dimen- sions. So integrate first over a bounded object, like, I dunno, a sphere or something. Then take the limit as the radius of the sphere goes to infinity.

That's the whole question. I think X can be anything as long as its a "bounded object".

Answer 1

Il first we a integrare over a sphere of a radius R and untertid centered at origin in S = { for (mito, ng )R3 : ** vi tre =R} a entett centred het x=rasind word = Assine sind z = sore ondern o no su osor ER Where Here du = = der der dez 8 8 simt do drded 2 e- p=0 dao 850 er27 I Pnh 4 T un je recondo - an early -25 (e-R"-1) = 2 (i-e-R") letting R a ne oo, we get I -leh dv = lim ann (1-e-R) R- 0 = 20