Actuarial Outpost Integration question
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#1
12-04-2017, 09:15 AM
 ch1rontl34 Member Join Date: May 2008 Posts: 144
Integration question

Hi everyone, I'm working on an MLC question but the question is actually calculus related. It's been many years since I passed P (career changer) and I can't seem to figure out this integration problem

I understand what u substitution is but I don't know how setting u=10-rootx leads to the 2 in the numerator. The steps in the attached picture are incomplete for my understanding, can anyone please help? Thank you!
Attached Images

Last edited by ch1rontl34; 12-04-2017 at 09:47 AM..
#2
12-04-2017, 09:34 AM
 Klaymen Member CAS Join Date: Oct 2001 Studying for AINS 21 & 22 Posts: 19,384

Can't read the problem with a graphic that small. Try putting the image in paint and cropping out the important parts.
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#3
12-04-2017, 09:35 AM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,012

Quote:
 Originally Posted by ch1rontl34 Hi everyone, I'm working on an MLC question but the question is actually calculus related. It's been many years since I passed P (career changer) and I can't seem to figure out this integration problem I understand what u substitution is but I don't know how setting u=10-rootx leads to the 2 in the numerator. The steps in the attached picture are incomplete for my understanding, can anyone please help? Thank you!
I can't see the picture clearly, but the 2 is probably associated with root x being x^(1/2) [and quite possibly then with the change of dx to du],
#4
12-04-2017, 09:48 AM
 ch1rontl34 Member Join Date: May 2008 Posts: 144

I have updated the attached file, sorry I didn't realize it showed up really small. I hope it's better now. Thanks to all who have responded already!
#5
12-04-2017, 10:01 AM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,012

Yes, what I expected. If

u = (10 - x^(1/2)) then

du/dx = -(1/2)x^(-1/2) so

du = -(1/2)[x^(-1/2)]dx

-2 du = [x^(-1/2)]dx

That last step is where the 2 comes from, also where the - in the numerator comes from.
#6
12-04-2017, 10:06 AM
 ch1rontl34 Member Join Date: May 2008 Posts: 144

I get it now, thanks Gandalf! I forgot about replacing dx in terms of du.