Final answer:
To find the volume of the solid under the surface z=8x+y² and above the region bounded by x=y² and x=y³, we need to integrate the given function over the region of interest.
Step-by-step explanation:
To find the volume of the solid under the surface z=8x+y² and above the region bounded by x=y² and x=y³, we need to integrate the given function over the region of interest.
First, we need to find the limits of integration by setting x = y² and x = y³ equal to each other. Solving this equation, we get y = 0 and y = 1 as the limits of integration for y.
Next, we integrate the function z = 8x + y² with respect to x from y² to y³, and then integrate the resulting expression with respect to y from 0 to 1. Solving these integrals will give us the volume of the solid.