1. (15 pts) Evaluate the following integral: 171*** v2 + y2 +7 derdy de
Evaluate the iterated integral by converting to polar coordinates. pV 32 – v2 V22 + y2 dx dy
5. (12 pts.) Evaluate the following triple integral where the region E lies above the cone 32+32 and below the sphere +y2 5. (12 pts.) Evaluate the following triple integral where the region E lies above the cone 32+32 and below the sphere +y2
Change the Cartesian integral to an equivalent polar integral, and then evaluate. 810 PV100 - y2 dx dy -10 - V100 - y2 A) 107 B) 1007 C) 2007 D) 4007 Evaluate the integral. ho 5x + 10y 25° 525-y? j*x + 10% de dx dy to dz dx dy 0 0 A) 625 B) 3125 C) 125 D) 25
3. (3 pts.) Convert the following double integral to an equivalent polar form but do NOT evaluate: 4-y2 3. (3 pts.) Convert the following double integral to an equivalent polar form but do NOT evaluate: 4-y2
10. (15 points) Evaluate the integral SSSE FDV with f = y2-2. E is the solid in the first octant that lies above the cone 2 = V x2 + y2 and below the sphere x2 + y2 + 22 = 1.
1. (5 points) Evaluate the line integral 1 + de todos dy, where C consists of the arc of the circle x2 + y2 = 4 from (0, 2) to (2,0).
Evaluate the following integral, Spz where S is the part of the sphere x2 + y2 +z2 16 that lies above the cone z = V5V - Evaluate the following integral, Spz where S is the part of the sphere x2 + y2 +z2 16 that lies above the cone z = V5V -
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)
Evaluate the following integral for a > 1 Sº 64x3 (x4 + 1) de 4a(a4 + 1). – 4.216 64a" (a4 + 1)– 64 - 215 1694 (a* + 1) 15 – 16. 215 (a4 + 1) 16 – 216
3.) a.) Evaluate the following integral. (15 points) in(1 +5x?) dx b.) Evaluate the following integral. (10 points) tanº (6x) sec 10 (6x) dx