I need help on calc 2

Question

find integrals

 

integrals that goes to 3 to 0

 

2/(9+x^2)dx   

 

 

Answer 1

I'm not sure if you meant 3-->0 or 0-->3 So I'll just show you how to get the integral and you can commute the answer.

 

∫2/(9+x²) dx

 

Familiarize yourself with some of common integral formats. These can be found in your text book or online review sheets. If you can remember these it makes things a lot easier.

 

Common integral format:

 

∫ 1/(a² + u²) du =  (1/a)tan^-1(u/a) + C

 

Since the integral is defined on 3-->0 you can ignore the constant C.

 

2 ∫ 1/(3² + x²) dx  = (2/3)tan^-1(x/3)

 

Then calculate from x = 3 to 0