wolfram-mathematicanumerical-integrationwolframalpha

Wolfram alpha, double integral over a plot or region


Im trying to do some homework in which they gave me a domain and a double integral.

I was trying to use wolfram alpha or symbolab to know how to do it but I can't get them to work, with wolfram I get to draw the domain but I dont know how to integrate with that domain, because I have the integral, which is ∫∫D( x2 + 5y2 )dxdy and the D is the Domain I have in the plot, so Im trying to search some way to tell wolfram you have this plot and you need to calculate this integral in this domain, but I don't know how.


Solution

  • To get WolframAlpha to integrate the function x^2+5y^2 over the domain you can use WolframAlpha notation to integrate over the outer semicircle and subtract the integral over the inner semicircle

    integrate x^2+5 y^2, {x,-4,4},{y,0,sqrt(16-x^2)} - integrate x^2+5 y^2, {x,-2,2},{y,0,sqrt(4-x^2)}

    link to the WolframAlpha page

    If calculations like this exceed either the line length limit or the computation time limit then you might do these as two separate calculations and then subtract the results as a final step.