Question

13. (5 points) Reverse the order of integration for the following iterated integral. You do not have to integrate. cos y dy dx 14. (5 points) Integrate the function g(r,0) = p sin over the sector of a disc in the first quadrant bounded by the circle r² + y2 = 1, the circle r² + y2 = 4, the line y = rV3, and the r-axis. 15. (5 points) Convert the following iterated integral from Cartesian to polar. You do not have to integrate. LWx2 + y2 dx dy 16. (5 points) Using spherical coordinates, set up, but do not integrate, the integral of the function h(x, y, z) = x over the bottom half of the solid sphere of radius 3 centered at the origin.

Answer 1

Sal“ – 13 4 14ge JES cosy. dyddlen ☺ 4-20 - old limit of se: H=o to ze=4 old limit of y: y=oto g=54-re =y=4-24 The region of integration is shocken 10, 2) y- as baended Gegroni To change order of entegration: cele make a strip parallel to taxts. coon se 1 (0-2) 1=4

Nowe Neces limid of y! y =o to y=2 - Neul limit of t. s=o to y 4-5 => x= 4-y? thes limit of this r=0 to se=4-4 using all this into ® - + - if any ordy. 4-y2. casy.dady. Ans.
As per HOMEWORKLIB POLICY I can answer only first question.