Almost finished with Calculus for ever

[Snakeonia]

i hope anyway lol here's my problem

Find area of Region cut from plane x + 2y + 2z = 5
by the cylinder whose walls are x = y^2 and x = 2 - y

can someone point me in the right direction

 

[HallsofIvy]

Start by drawing a picture- what do the graphs of x= y² and x= 2- y look like? Where do they intersect? If you were integrating over that region, what would the limits of integration be? And, of course, you want to integrate the "differential of area" for the plane x+ 2y+ 2z= 5. Since that is a plane, there are several different ways of computing that. What have you tried?