Use cylindrical or spherical coordinates, whichever seems more appropriate. Evaluate ∫∫∫E z dV, where E lies above the paraboloid z = x2 + y2
and below the plane z = 2y. Use either the Table of Integrals or a computer algebra system to evaluate the integral.

Step-by-step explanation:

The region E that lies above the paraboloid : z = x^2 + y^2

while the region E that lies below the paraboloid : z = 4y

equate the two equations to get the representation of the curves

x^2 + y^2 = 4y = x^2 + ( y -2 )^2 = 4

the polar form will be : r = 4sin∅

attached below is the remaining part of the solution

answer: give more info

step-by-step explanation:

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.