How do you find the integration limits of this triple integral

The function to integrate is f(x,y,z)=xy^2z^3 over the region limited by the surface z=xy and the planes y=x, x=1 and z=0.

Can you explain how to find the integration limits for each of the three integrals?

order of integration dz dy dx

z is from 0 to xy

y is from 0 to x

x is from 0 to 1

after integrating with respect to z, you get

(1/4)x y^2 z^4 from 0 to xy

= (1/4)x y^2 (x^4 y^4 )

= (1/4) x^5 y^6

after integrating with respect to y, you get

(1/4)(1/7)x^5 y^7 from 0 to x

= (1/28) x^5 x^7

= (1/28) x^12

now integrate with respect to x

= (1/28)(1/13) x^13 from 0 to 1

= (1/28)(1/13)

= 1/364