# triple integral

Calculus III Homework 13 Solve the following exercises. Show your work. (No credit will be given for an answer with no supporting work shown.) #1. Evaluate the triple integral SSS ** xy2dV, B where B is given by B = {(x,y,z):2 5×53, -1 Sys0, -2 52 51}. #2. Evaluate the triple integral SSS x2 xdV, where E is given by E = {(x,y,z):2 5x 22, 0 5 y 5x+2, 15252}. #3. Set up the iterated integral to evaluate the triple integral SSS (x2 + y2) dv, . E where E is the solid bounded by the paraboloid z = x2 + 4y2 and the plane z = 9. Do not evaluate the integral. (a) Use the order of integration dx dy dz (b) Use the order of integration dy dz dx #4. Use cylindrical coordinates to evaluate the integral 4-32 SIS 3+ 2×2 + 2y2 dz dy dx 4-x2 #5. Find the rectangular coordinates of the point (3,570/4, 1/6) given in spherical coordi- nates. #6. Find the spherical coordinates of the point (1,- ,-1, V2/3) given in rectangular coordi- nates. #7. Use spherical coordinates to set up the iterated integral to evaluate the triple integral SIS 3xz dv, E where E is the solid between the spheres centered at the origin of radii 3 and 5 with x > 0. Do not evaluate the integral.

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