Double numeric integral of a function help please

Hello everyone

I want to numerically integrate a function

1-x^2-y^2

Where x^2+y^2<=1 circular area

What I tired so far is First try:

quad2d(@(x,y) 1-x^2-y^2, -1,1,-1,sqrt(1-x^2))
Second try:

syms x y
int(int(1-x^2-y^2,y, -1,sqrt(1-x^2))x,-1,1)

How can I use sqrt(1-x^2) as the boundary of the integral for y?

I know this can be done with r and theta but I want to calculate the integral by cartesian coordinates.

Could someone offer a solution?

Answer 1

[Roger Stafford]

You need to make the integration limit sqrt(1-x^2) a function handle. See the documentation at

     http://www.mathworks.com/help/matlab/ref/quad2d.html

In particular note where it says "q = quad2d(fun,a,b,c,d) approximates the integral of fun(x,y) over the planar region and fun is a function handle, c and d may each be a scalar or a function handle."

[Youssef Khmou]

it did not work yet, you have dblquad function?

f=@(x,y) 1-(x.^2)-(y.^2);
w=@(x) sqrt(1-x.^2);
q=dblquad(f,-1,1,-1,w);

Answer 2

[bogazici guvercin]

Thanks for the help

The function handle is not working with dblquad somehow but working with quad2d.

Thanks for the help!