Midterm 1: Math 30, 9/20/07
1) A region is formed by 2
4
1xy = and y=x
a) Sketch the region
b) Find the area between two curves.
c) If the region is rotated about the x axis find the volume of the solid
2) A region is formed by y = 6x – x2 and x = 0
a) Sketch the region
b) Find the area of the region
c) If the region is rotated about the x-axis, find the volume of the solid
d) If the region is rotated about the y=axis, find the volume of the solid
3) A spring with constant k = 5 N/m and rest length of .05 m is stretched additional .025
m. Find the work done. F=k(x-x0)
4) Temperature varies as )
24
sin(510)( ttT
π
+= during the day where t is in hours. What
is the average temperature during 24 hours?