11. Use polar coordinates to evaluate the integral 1,8-2V(+ y2)<dy dx
5.Use polar coordinates system to evaluate: x2 + y2)dydx , R is the region enclosed by 0 <x< 1 and, -x sy sx
3. Draw the region D and evaluate the double integral using polar coordinates. (a) SI x + y dA, x2 + y2 D= {(x, y)| x2 + y2 < 1, x + y > 1} D (b) ſ sin(x2 + y2)dA, D is in the third quadrant enclosed by m2 + y2 = 71, x2 + y2 = 27, y=x, y= V3x.
3. Draw the region D and evaluate the double integral using polar coordinates. dA, D= {(x, y)| x2 + y² <1, x +y > 1} (b) sin(x2 + y2)dA, D is in the third quadrant enclosed by D r? + y2 = 7, x² + y2 = 24, y = 1, y = V3r.
Evaluate the iterated integral by converting to polar coordinates. pV 32 – v2 V22 + y2 dx dy
Use cylindrical coordinates to evaluate the integral. S SVO?-?? /o-+?=> p?dzaydx (a > 0) Enter the exact answer. S6 Soy Sa+=2=x?dzdydx ? Edit Use cylindrical or spherical coordinates to evaluate the integral. 36—y2 2-x2y2 6* %* Son z? dz dx dy Enter the exact answer. 6.* 6*** San z2 dz dx dy = x2 + y2
Change the Cartesian integral to an equivalent polar integral, and then evaluate. ss dx dy -V16-y2 1+122 7:18 +2 1n 5) 2 (8 +2 In 5) 4 (8 + In 5) 78 +in5) 2
Do not evaluate, rewrite the integral using spherical coordinates 25-x² - y2 1 dz dx dy 05 NUS y=0 X-O Z=o
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
1. Use cylindrical coordinates to SET UP the integral for the volume of the portion of the unit ball, 22 +232 + x2 < 1, above the plane z = 12 2. (a) Write in spherical coordinates the equations of the following surfaces: (i) x2 + y2 + x2 = 4 (ii) z = 3x2 + 3y2 (b) SET UP the integral in spherical coordinates for the volume of the solid inside the surface 22 + y2 + x2 =...
2. Use cylindrical coordinates to solve the integral SSS (x2 + y2) dx dy dz D Z 2 Z = 2 z=Ż (x2 + y2) tor - y Х