Looking for Help with HS Math problems

[yeskayglobal]

My daughter was given following problems to solve... It is beyond my comprehension. Can someone help or point me to someone who can help.

1. Evaluate ∫∫ Sin π (x2 - y2) dA, where R is the region bounded by hyperbolas x2 - y2 =1, x2 - y2=4, and the lines x - y=1 and x - y=2.
R


2.a. If C is the line segment connecting the point (x1, y1) to the point (x2, y2), show that
∫ -y dx + x dy = x1y2 - x2y1.
C

b. Use Green's theorem and part and part (a) to find the area of the pentagon with vertices (0, 0), (2, 1), (1, 3), (0, 4), and (-1, 1)

 

[Romsek]

You should probably have your daughter go ahead and ask this herself. There will probably be some (lots) of back and forth and there's no reason you have to be a go between. If she's doing Green's theorem she's either quite the prodigy or she's old enough to interact with folks here.