Use a double integral to find the volume of the indicated solid. z = 1-xy, y=x, y=1
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Inferred integral to find volume of indicated solid
int_(0)^(1)int_(0)^(y)(1-xy)dxdy
Integration with respect to x
int_(0)^(1)[x-(x^(2)y)/(2)]dy
Evaluation with respect to x
int_(0)^(1)(y-(y^(3))/(2))dy
Integration with respect to y
(y^(2))/(2)-(y^(4))/(8)
Evaluation with respect to y
(3)/(8)
Result:
(3)/(8)