Evaluate ∫sin(x^2 + y^2) dA where R is the disk of radius 13 centered at the origin.?

May 2021 2 121 Report

Evaluate ∫sin(x^2 + y^2) dA where R is the disk of radius 13 centered at the origin.?

Idk i figured itd be something like ∫∫sin(x^2 + y^2) rdrdø but i dont know what the limits are or how to solve it :(

help?

The disk x^2 + y^2 ≤ 13^2 transforms to r^2 ≤ 13^2 ==> r ≤ 13 in polar coordinates.

So, ∫∫ sin(x^2 + y^2) dA

= ∫(θ = 0 to 2π) ∫(r = 0 to 13) sin(r^2) * r dr dθ, converting to polar coordinates

= 2π * (-1/2) cos(r^2) {for r = 0 to 13}

= π(1 - cos 169).

I hope this helps!