3. Use spherical coordinates to calculate this integral of f(x, y, z)=√√² + y² + 2² over the region ² + 51, z 20. y² +²54,

Justify the Fundamental Theorem of Line Integrals for F. dr in the case when F(x, y) = (8x + 8y)i + (8x + 8y)j and C is a portion of the positively oriented circle x2 + y = 25 from (5, 0) to (3, 4). F. dr =

Evaluate the line integral fa xds where C is one quarter of a circle (in the first quadrant) of radius 5 centered the origin with movement occuring in the counterclockwise direction.

Use Green's Theorem to evaluate the line integral of F = (x6, 3x) around the boundary of the parallelogram in the following figure (note the orientation). (xo.) (X0.0) Sex6 dx + 3x dy = (2x-Y) ·x With xo = 7 and yo = 7.