Question

Can someone please look at my drawing and tell me if I separated the integral correctly? Thanks!

The computer said I was wrong because x^4+2x^2+1 is a perfect square of (x^2+1)^2...and they got a different answer...if they are right, can you tell me why I am wrong? Isn't it okay to integrate without completely factoring it down?

Answer 1

I just don't understand why I am wrong!

Answer 2

you can't break up the square root. you have to keep it as.

\[\sqrt{x^4+2x^2+1}\]

this is (x^4+2x^2+1) = (x^2+1)^2 which when square rooted gives you x^2+1, which is a much simpler integral.

Answer 3

if you look at the drawing I just posted, I think that is the correct way, but I just dont understand the rule as to why I can't integrate without making it a perfect square first?

Answer 4

It's almost like if you don't completely factor your integrand first, it will ALWAYS be wrong...is this a correct way of looking at things?

Answer 5

sqrt(x^4+2x^2+1) is not the same as sqrt(x^4)+sqrt(2x^2)+sqrt(1).

Answer 6

oh...so I just did an Algebra mistake there?

Answer 7

yes.

Answer 8

yikes! haha...no wonder I got it wrong! I do have a simple question though...

Answer 9

as a rule of thumb...do you ALWAYS have to factor completely your integrand?

Answer 10

no, but in this case it made the problem easier.

Answer 11

ok...got it! Thanks tomo! Here is your medal!

Answer 12

You MUST have your algebra working better than that. How can you learn calculus if you are spending time learning algebra? Prictice more. Break out your algebra book. Work another 1000 algebra problems.

Answer 13

@SinginDaCalc2Blues sometimes we all have brain blocks. no worries.