# Integrals, moment of inertia, and Stokes theorem

See attachment for fomatting

1

Evaluate

3∫1

1-∫-2

(x2y-2xy3)dydx

2

Correctly reverse the order of integration, then evaluate

1∫0

1∫y

xeydxdy

3

The plane region R is bounded by the graphs of y=x and y=x2 .

Find the volume over R and beneath the graph of f(x, y) = x + y.

4

Find the volume of the "ice cream cone" bounded by the sphere x2+y2+z2=1 and the cone

z

=

^/Â¯x2+y2-1

5

Find the moment of inertia around the z-axis of the solid bounded by

x = 0, y = 0, z = 0, y = 1 - x2, and 4x + 3y + 2z = 12, assume _(x,y,z)_1.

6

Evaluate ∫CP(x,y)dx+Q(x,y)dy

Given: P(x,y)=y2, Q(x,y)= 3x; C is the part of the graph of y=3x2 from (-1,3) to (2,12).

7

Use the divergence theorem to evaluate

∫∫s F?nds where n is the outer unit normal vector to the surface S. ∫∫F = 3xi + 2y2j + 4zk;

S is the surface of the plane x + y + z = 6.

8

Use Stokes theorem to evaluate W = F?Tds where F(x, y, z) = 3yi - 2xj +4xk; C is the circle: x2 + y2 = 9, z = 4,

oriented counterclockwise as viewed from above.

https://brainmass.com/math/integrals/integrals-moment-of-inertia-and-stokes-theorem-180872

#### Solution Summary

This is a series of calculus problems that involve Stokes theorem, finding volume of solids, and moment of inertia