scan it clear please 6. (15points ) Evaluate the triple integral cln(y+1) е-2" dr dy dz....
8. Clearly construct a triple integral of the form dz dy dr to find the volume of the solid shown. The solid is constructed by taking the paraboloid :=x2 + y and have the top cut by the plane z=4y. But do not evaluate the integral. 1 10 8 ry
Clearly construct a triple integral of the form dz dy dx to find the volume of the nose of a vehicle constructed from the paraboloid y=2(x +z) and the vertical plane y=6. But do not evaluate the integral.
3. Consider the triple integral 2z sin(x2 + y2 +22 - 2x) dy da dz. Set up, but do not evaluate, an equivalent triple integral with the specified integration order. a) (6 pts) da dz dy b) (7 pts) dz dr de (Cylindrical Coordinates) c) (7 pts) dp do do (Spherical Coordinates)
please provide algebric details 7. Clearly construct a triple integral of the form dz dy dx to find the volume of a solid constructed by joining 2 paraboloids J==18- x - y? . But do not have to evaluate the integral. (==x² + y² 2-18-x - y
4. Rewrite the following triple integral so that the order of integration is dy dx dz. Do not evaluate it. (3x + y) dz dy dit
Question 17 Evaluate the triple integral: 3x +2y dz dy dx SST*** Write your answer as a decimal number rounded to 2 decimal places.
y2 + 4z2 = 16 Clearly construct a triple integral of the form dz dy dx to find the volume of the solid shown. The upper surface is defined by the cylinder y? +422 = 16. But do not evaluate the integral. 4 x
Consider the triple integral LLL 3- 2z sin(x² + y2 + 22 - 2x) dy do dz. -3-2- Set up, but do not evaluate, an equivalent triple integral with the specified integration order. a) (6 pts) do dz dy b) (7 pts) dz dr do (Cylindrical Coordinates) c) (7 pts) dp do do (Spherical Coordinates)
Q3. Sketch the region of integration for the integral [5(8,19,2) dr dz dy. (2, y, z) do dzdy. Write the five other iterated integrals that are equal to the given iterated integral. Q4. Use cylindrical coordinates and integration (where appropriate) to complete the following prob- lems. You must show the work needed to set up the integral: sketch the regions, give projections, etc. Simply writing out the iterated integrals will result in no credit. frs:52 (a) Sketch the solid given...
LL L'Amazz de de dy= L*IL 4az dz dx dy = Edz dr de y Jv+y MMMMMM 0 = 02 = Evaluate the integral 4xz dz da dy =