The figure below shows the region of integration for the int

The figure below shows the region of integration for the integral. Integral_0^1 integral_y^1integral_0^z f(x, y, z)dxdydz Give the five other iterated integrals that are equal to this integral.

Solution

consider all sequences of dx dy dz and corresponding see the limits of x y z

given for dx dz dy x is 0 to z z is y to 1 and y is 0 to 1

now for lets say dx dy dz x is o to z y is z to 1 and z is 0 to 1

now for dy dz dx y is 0 to z z is x to 1 and x is 0 to 1

now for dy dx dz y is 0 to z x is 0 to z and z is 0 to 1

now for dz dy dx z->y to 1 y is x to 1 x is 0 to 1