Answer:
0
Step-by-step explanation:
If we use polar coordinates, the region D can be covered by replacing (x,y) by (r*sin(Θ),rcosΘ)), with 0<r<7, 0<Θ<2π. The differential matrix
has determinant equal to r, so we can compute the double integral as follows
(Note that we multiplied by the determinant of the Jacobian, r). A primitive for r³ is r⁴/4, thus, for Barrow's rule we have
A primitive of cos(Θ)sin(Θ) can be obtained using substitution, and it is sin²(Θ)/2 (note that the derivate of sin²(Θ) is 2sin(Θ)cos(Θ)). Therefore, taking both the dividing 4 and the 2 obtained, we have
Hence, the integral is 0.