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[✓] Calculate a double integration of two functions?

GROUPS:

Hi, all! So basically I'm trying to do a double integration of two functions but in one case Mathematica outputs "Null" in the answer while in the other case it outputs the same input and doesn't really do anything.

Here below are snapshots of code and the output given by Mathematica.

  1. https://imgur.com/a/XtBu0

  2. https://imgur.com/a/KAwep

Thanks in advance :)

POSTED BY: Raivat Shah
Answer
27 days ago

Hello

First integral can't be solved symbolically. Integral with gamma function has no antiderivative with standard elementary function or maybe known special function, no discovery yet. Use NIntegrate,a numericall integrator.

 NIntegrate[Gamma[n + 1]/Gamma[k + 1]*1/Gamma[n - k + 1]*(1/10000)^k, {n, 25,  500}, {k, 2, 25}]
 (* 0.0481051 *)

Second integral, you did little mistake in syntax.

Integrate[(x*y^2)*(1/(x^2 + 1)), {x, 0, 1}, {y, -3, 3}]
(* Log[512] *)

Regards Mariusz

PS: Next time post code not image.SEE

POSTED BY: Mariusz Iwaniuk
Answer
27 days ago

Dear Mariusz Iwaniuk,

Thank you so much for your response. It was a great help :) However, for the second part where you mentioned removing the comma, I get a different answer when I do the same thing by hand. When I do it manually, I get the answer as "9 ln 2" instead of "Log [512]"

I realise that 9 ln 2 = ln 512, but aren't Log and Ln different?

Sorry for the confusion, I'm a complete beginner to Mathematica.

Thank you so much, Raivat S.

POSTED BY: Raivat Shah
Answer
27 days ago

In Mathematica Log[z] gives the natural logarithm of z (logarithm to base e) and Log[b,z] gives the logarithm to base b.

Log[512]//PowerExpand
(*  9 Log[2] *)
POSTED BY: Mariusz Iwaniuk
Answer
27 days ago

Please make sure you know the rules: https://wolfr.am/READ-1ST

Do NOT post code as images.

POSTED BY: Moderation Team
Answer
27 days ago

Oops, sorry I'm a complete beginner. I will make sure that this doesn't happen again.

POSTED BY: Raivat Shah
Answer
27 days ago

Group Abstract Group Abstract