Rewrite the integral 12-6y 2 ALF -1 f(x, y, z) dz dy dx
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- Find the centroid of the thin plate bounded by the graphs of g(x)=x and f(x) = x + 6. Use the equations shown below with 8 = 1 and M = area of the region covered by the plate. == b f a M Sx[f(x) - g(x)] dx b y=-=-=[r²(x)-g²(x)] dx The centroid of the thin plate is (x,y), where x = (Type integers or simplified fractions.) and y =Find div F and curl F if F(x, y, z) = xzºi + 6y²x²j + 6z²yk. div F= curl F=The area of the region completely bounded by the curve y = 23 the x-axis, and the line containing the points (a, 0) and (2, 2) is Determine the value of a. 1 y = (2, 2) (a, 0)
- Plz integrate # 3and # 4…plz plzy (1, 1) X=1 y=x² C X (0,0) Region A is bounded by the parabola x = y², the line y = 1, and the y-axis. Region B is bounded by the parabolas x = y² and y = x². Region C is bounded by the parabola y = x², the line x = 1, and the x-axis. 1. What is the area of A? A. squnit B. 2 squnit C. squnit D. 3 squnit 2. What is the area of B? A. squnit B. 3 squnit C. squnit D. squnit 3. What is the area of C? A. 2 squnit B. squnit C. squnit D. / squnit 4. What is the volume of the solid generated when region C is revolved about the x-axis? A. V≈ 0.63 c. u. B. V≈ 0.72 c. u. D. V≈ 0.92 c. u. C. V≈ 0.84 c. u. 5. What is the volume of the solid generated when region B is revolved about the y-axis? A. V 2.13 c. u. B. V≈ 0.94 c. u. C.V ~ 1.27 c. u. D. V 3.08 c. u. y = 1 x = y² BFind the area bounded by the curve y = x² and y = x+ WRITE THE GIVEN AND DETAILED SOLUTION