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

[defineNormal]

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]

You're close.. just the factor infront is incorrect. From your example, you know that the general rule is $$\int x^n dx = \frac{1}{n+1} x^{n+1} + C$$ Try and fit your specific case into this, and you should come out with the correct constant in front.

 

[d_leet]

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?

 

[defineNormal]

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]

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]

You are takinb calculus and you are telling us you cannot add $1+ \frac{1}{2}$?? Am I misunderstanding this?