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X^2+2 were integrated it would be 1/3x^3

Hello I'm trying to integrate Ar^(1/2)

would the answer be?

well I know if X^2+2 were integrated it would be 1/3x^3

I just get confused when it's fractions would it be

(3/4)Ar^(3/2)???
 

cristo

Staff Emeritus
Science Advisor
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You're close.. just the factor infront is incorrect. From your example, you know that the general rule is [tex] \int x^n dx = \frac{1}{n+1} x^{n+1} + C [/tex] Try and fit your specific case into this, and you should come out with the correct constant in front.
 
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1
Hello I'm trying to integrate Ar^(1/2)

would the answer be?
It depends what you are integrating with respect to. Are you integrating with respect to r?

well I know if X^2+2 were integrated it would be 1/3x^3
You forgot to integrate half of that function, your answer would be correct for integrating just x^2 but you didn't integrate the 2.

I just get confused when it's fractions would it be

(3/4)Ar^(3/2)???
If you are integrating with respect to r then this is almost correct, but your fraction isn't quite right. What is the rule when you integrate x to a power?
 
well it's A*r^(1/2), for example a+bt+bt^2= a^2/2*bt^2/2*bt^3/3, I'm just not good w/ fractions, would it be Ar^(3/2)/(3/2)? or (3/2)Ar^(3/2)?
 

cristo

Staff Emeritus
Science Advisor
8,056
72
well it's A*r^(1/2), for example a+bt+bt^2= a^2/2*bt^2/2*bt^3/3, I'm just not good w/ fractions, would it be Ar^(3/2)/(3/2)? or (3/2)Ar^(3/2)?
You're correct with Ar^(3/2)/(3/2) but you need to add the constant of integration, so the solution is (2/3)*Ar^(3/2) +C
 

HallsofIvy

Science Advisor
Homework Helper
41,665
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You are takinb calculus and you are telling us you cannot add [itex]1+ \frac{1}{2}[/itex]?? Am I misunderstanding this?
 

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