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URGENT Can someone answer these two questions within the next hour? Use Green’s Theorem to find...

URGENT

Can someone answer these two questions within the next hour?

Use Green’s Theorem to find the integral of the vector field F~ (x, y) = (5y + 4x)~i + (3y − 7x)~j counterclockwise around the ellipse x 2 9 + y 2 = 1. Hint: The area of the ellipse with equation x 2/ a 2 + y 2 /b 2 = 1 is πab.

Use Stokes’ Theorem to compute Z C F~ · d~s where F~ (x, y, z) = y 2~i + z 2~j + x~k and the curve C is the triangle in 3-space with vertices at (1, 0, 0), (0, 1, 0), and (0, 0, 1). Hints: (a) For the surface S needed in Stokes’ Theorem, use the part of the plane x + y + z = 1 that lies in the first octant. (b) That plane can be written parametrically as Φ(x, y) = hx, y, 1 − x − yi. (c) Make sure you have the upward pointing normal!

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