courtesy of David J. Manuel
Section 7.1-7.2
d
1. Define g ( y ) dy using a general partition. Given g ( y ) > 0, interpret the integral as it relates to c the graph of x = g ( y ).
2. Interpret
Z
−
− 1
√
2
2
√
1
− x
2 dx +
Z
−
0
√
2
2
− x dx as the area of a region. Write an integral in terms of for this region and use area to compute the integral.
y
3. Interpret
Z
0
π
(cos x
− sin x ) dx as a difference of areas. Describe the regions as specifically as possible.
Section 7.2
4. Write a Riemann Sum definition to find the volume of the solid obtained by rotating the region bounded by x = 2 y
− y
2 and x = 0 about the y -axis.
5. Derive a formula for the volume of the frustrum of a cone which has a height h , smaller radius r , and larger radius R .
r h
R
6. Given f ( x )
≥
0 on [ a, b ], write an integral formula to find the volume of the solid formed by rotating the region bounded by y = f ( x ) , y = 0 , x = a , and x = b about the line y = M , where M is the maximum value of f on [ a, b ].