Please help now 9 is the rectangle with vertices (0, 0), (3, 0), (3, 4),and (0,4)6. fc (x² + y²) dx + (x² - y²) dy,C is the triangle with vertices (0, 0), (2, 1), and (0, 1)7. fc (y + e√) dx + (2x + cos y²) dy,C is the boundary of the region enclosed by the parabolasy = x² and x = y²8. fcy¹ dx + 2xy³ dy,C is the ellipse x² + 2y² = 29. Scy³ dx - x³ dy, C is the circle x² + y² = 410. fc (1 - y³) dx + (x³ + ey²) dy, C is the boundary of theregion between the circles x² + y² = 4 and x² + y² = 911-14 Use Green's Theorem to evaluate e F. dr. (Check theorientation of the curve before applying the theorem.)30011. F(x, y) = (y cos xxy sinx, xy + x cos x),C is the triangle from (0, 0) to (0, 4) to (2, 0) to (0, 0)12. F(x, y) = (ex + y², e³ + x²),C consists of the arc of the curve y cos x from (-π/2, 0)to (π/2, 0) and the line segment from (7/2, 0) to (-T/2, 0)1113. F(x, y) = (y - cos y, x sin y),C is the circle (x − 3)² + (y + 4)² = 4 oriented clockwise14. F(x, y) = (√x² + 1, tan¯¹x), C is the triangle from (0, 0)to (1, 1) to (0, 1) to (0, 0)CAS 15-16 Verify Green's Theorem by using a computer algebrasystem to evaluate both the line integral and the double integral.15. P(x, y) = x³y4, Q(x, y) = x³y4,C consists of the line segment from (-7/2, 0) to (π/2, 0)followed by the arc of the curve y = cos x from (π/2, 0) to(-TT/2, 0)16. P(x, y) = 2x - x³y³, Q(x, y) = x³y8,C is the ellipse 4x² + y² = 417. Use Green's Theorem to find the work done by the forceF(x, y) = x(x + y) i + xy² j in moving a particle from theorigin along the x-axis to (1, 0), then along the lineto (0, 1), and then back to the origin along the y-axis.segmentcycloid and us21. (a) If C is thethe point (S(b) If the vertiare (x₁, y₁.the polygoA = 1/[(x₁(c) Find the a(1, 3), (0,22. Let D be a regxy-plane. Usenates of the ce12Awhere A is thex =23. Use Exerciseregion of radi24. Use Exercisevertices (0, 0)25. A plane laminregion in theShow that itsIx = -26. Use Exercisedisk of radius(Compare wit27. Use the methoFand C is any Eencloses the c28. Calculate fe FC is the SILI

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∫Cy3dx-x3dy ,C is the circle x2+y2=4

9. Scy³ dx - x³ dy, C is the circle x² + y² = 4 10 (1 3) v21