Question

Find the volume of the solid bounded by the coordinate planes and the plane 7x + 8y + z = 6.

I'm having trouble finding the bounds for the double integral.

Answer 1

use zeros to find the maximum values of each individual element:
0 + 0 + z = 6 implies 0 <= z <= 6
0 + 8y + 0 = 6 implies 0 <= y <= 3/4
7x + 0 + 0 = implies 0 <= x <= 7/8

since it's a plane, it will be a triangular pyramid, and you'll also be able to calculate the volume directly, V = 1/6xyz (V = 1/3bh, b = 1/2xy)

Answer 2

Thank you. I figured it out when you said it would be a pyramid. I just set the bounds of dy to be from 0 to (-7/8)x+(3/4).