Need Help with Integration for Astronomy Class?

[b_o3]

Hi, I have to do a lot of integration questions for my astoronomy class but I'm not really sure how to! for example how do u integrate from a number let's say a = 0, to a = 1/(1+z)... and dt = \frac{da}{H_0 \left(\frac{\Omega_{m,0}}{a} + a^2 \Omega_{\Lambda,0}\right)^{\frac{1}{2}}}

I've done a different kind of simple integration but i have no idea how this works,. thanks!

 

[AKG]

Hi, I have to do a lot of integration questions for my astoronomy class but I'm not really sure how to! for example how do u integrate from a number let's say a = 0, to a = 1/(1+z)... and dt = \frac{da}{H_0 \left(\frac{\Omega_{m,0}}{a} + a^2 \Omega_{\Lambda,0}\right)^{\frac{1}{2}}}

I've done a different kind of simple integration but i have no idea how this works,. thanks!

You want to know how to compute:

\int _0 ^{(1+z)^{-1}}\frac{da}{H_0 \left(\frac{\Omega_{m,0}}{a} + a^2 \Omega_{\Lambda,0}\right)^{\frac{1}{2}}}

 

[AKG]

You can use this site to compute the indefinite integral for you. Note that the variable of integration it uses is x, so you'll have to replace all your a's with x's. For the constants H_0,\, \Omega _{m,0} ,\, \Omega _{\Lambda ,0} just put in b, c, and d. The final answer it gives you might look ugly, but it can easily be simplified (there are factors on the top and bottom that should cancel right away). Given the answer, you can differentiate it to see that it is indeed the indefinite integral. However, I don't know a general method you can use if you wanted to compute it yourself. Anyways, once you have the indefinite integral, you just need to plug in (1+z)^-1 and 0, then subtract, to get the desired definite integral.