- 1 Integrate The Function F X Y X 2y Over The Rectangle 0 2 0 2 20 X Y Da Where D Is The Triangular 1 (111.36 KiB) Viewed 74 times
1. Integrate the function f(x, y) = x - 2y over the rectangle [0, 2] × [0, 2). // (20 (x+y)dA where D is the triangular region bounded by the x-axis, the y-axis, and the 2. Evaluate D line x + y = 1. 3. Use polar coordinates to evaluate JS D X and x > 0. 4. Evaluate the following triple (iterated) integral 24 3 ||| 1 1 (x, y, z) d(u, v, w) 8. Evaluate the scalar line integral √x² + y² 5. Use cylindrical coordinates to find the integral x² + y² between the planes z = 0 and z = 2. 7. Find Jacobian dA where D is semicircle bounded by x² + y² ≤ 1 1-y Z - dx dy dz. Hint: the inequalities defining E are x² + y² <4 and √² + y² ≤z≤ 2. 6. Use spherical coordinates to find the volume of the region defined by 4 ≤ x² + y² + z² ≤9. We zdV where E is the region inside the cone z² : if x=u² + 2vw, y = w³ - wv, z = sin w. Solar (x + z²)ds where C is the curve (sint, cost, 2t) for 0 ≤ t ≤ π. 9. Evaluate the vector line integral [(yda - rªdy) where C is the curve parametrized by r(t) = (t, t² – t) for 0 ≤ t ≤ 1. 10. Find the flux of the vector field F = xi+yj across the circle x² + y² = 4 oriented counterclockwise.