1. Find the volume of the solid that lies under the surface z=1+x y, and above the region D in the x y-plane, where D is a triangle with vertices (0,0),(1,1), and (0,1).

Question

Accepted Answer

Step:1 ：The volume of the solid under the surface (z=f(x,y)) and above the region (D) in the (x y)-plane is given by the double integral (int int_D f(x,y) , dx , dy).Step:2 ：In this case, (f(x,y)=1+xy) and (D) is the triangle with vertices ((0,0),(1,1)), and ((0,1)).Step:3 ：We can integrate over (D) by integrating (x) from (0) to (y) and (y) from (0) to (1).Step:4 ：The volume of the solid is calculated to be (frac{5}{8}).Step:5 ：Final Answer: The volume of the solid that lies under the surface (z=1+x y), and above the region (D) in the (x y)-plane, where (D) is a triangle with vertices ((0,0),(1,1)), and ((0,1)) is (boxed{frac{5}{8}}).

Answer

Step: 1 ：The volume of the solid under the surface (z=f(x,y)) and above the region (D) in the (x y)-plane is given by the double integral (int int_D f(x,y) , dx , dy).Step: 2 ：In this case, (f(x,y)=1+xy) and (D) is the triangle with vertices ((0,0),(1,1)), and ((0,1)).Step: 3 ：We can integrate over (D) by integrating (x) from (0) to (y) and (y) from (0) to (1).Step: 4 ：The volume of the solid is calculated to be (frac{5}{8}).Step: 5 ：Final Answer: The volume of the solid that lies under the surface (z=1+x y), and above the region (D) in the (x y)-plane, where (D) is a triangle with vertices ((0,0),(1,1)), and ((0,1)) is (boxed{frac{5}{8}}).

1. Find the volume of the solid that lies under the surface $z = 1 + x y$ , and above the region $D$ in the $x y$ -plane, where $D$ is a triangle with vertices $(0, 0), (1, 1)$ , and $(0, 1)$ .

Answer

Popular Problems

1. Find the volume of the solid that lies under the surface z=1+xy, and above the region D in the xy-plane, where D is a triangle with vertices (0,0),(1,1), and (0,1).

Answer

Popular Problems

1. Find the volume of the solid that lies under the surface $z = 1 + x y$ , and above the region $D$ in the $x y$ -plane, where $D$ is a triangle with vertices $(0, 0), (1, 1)$ , and $(0, 1)$ .