Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations. z = xy, z = 0, y = x, x =1, first octant.

1/8

Step-by-step explanation:

Given:

z = xy

z = 0

y = x

x =1

To find:

volume of the solid bounded by the graphs of the equations

Solution:

Compute integral of volume in the first octant:

= x y²/2 |ˣ₀  dx

= 1/2   x y² |ˣ₀  dx

= 1/2   x (x²-0²) dx

= 1/2   x³dx

=   |¹₀

= (1/2) (x⁴/4) |¹₀

= 1/8 x⁴ |¹₀

= 1/8 (1⁴ - 0⁴)

= 1/8 (1)

V = 1/8

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step-by-step explanation: