Evaluate the line integral by the two following methods. fxy dx + 2 dx + x²y³ dy C is counterclockwise around the triangle with vertices (0, 0), (1, 0), and (1, 2) (a) directly (b) using Green's Theorem

Evaluate S (xy + x + 2) ds along the curve r(t) = 2ti + tj + (3 − 2t)k, Osts 1. Sc (xy + x + 2) ds = x+z) ds = (Simplify your answer.)

Let y be the hypocycloid (t) = (8 cos³ t, 8 sin³ t), t = [0, 2π], and let C be the portion of y from the point (8,0) to the point (0,8). (a) Determine the length of y. Jov с (b) Evaluate √x ds. (0,8) (8,0)

c. Let P(x, y) = y² + sin¬1 x² and Q (x, y) = 2xy + 4x. Suppose that C is the parallelogram with vertices (0,0), (4,0), (1,3) and (5,3). Evaluate f rax Pdx + Qdy over C

Two numbers are greater than 10 but less than 40. Their GCF is 17. What are the two numbers?

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