Surface integral of a scalar function in the first octant

I am having difficulty drawing and parameterizing the surface for the integral $$\iint_s x^2z\,dS\$$ s: 1st octant part of $$y=x^2\$$ cut by $$2x+y+z=1$$

• Where do y=x^2 and 2x+y+z=1 intersect? – Saketh Malyala Apr 20 at 1:40
• There are 2 possibilities for the area s. It also has to be specified whether s is with the yz plane or xz plane before getting an answer. – KY Tang Apr 20 at 3:05
• I wrote down the question wrong as dxdy should have been dS but other than that, its all the information given to me in the question. – Terry Lay Apr 21 at 2:26