3
1. Let ππ be a function deοΏ½ined by ππ(π₯π₯) = 2π₯π₯ 2 −7π₯π₯+5. Find the slope of the line tangent to
the graph of ππ at π₯π₯ = 3.
3
2. Let ππ be a function deοΏ½ined by ππ(π₯π₯) = 2π₯π₯ 2 −7π₯π₯+5.
Evaluate
οΏ½
∞
5
3
2π₯π₯ 2 − 7π₯π₯ + 5
ππππ
3. Consider the region bounded by the π₯π₯-axis, the line π₯π₯ = 2, and the
π₯π₯ 3
curve ππ(π₯π₯) = √4+π₯π₯ 2. Find the area of this region.
4. Given the region bounded by the graphs of π¦π¦ = π₯π₯ sin π₯π₯ , π¦π¦ = 0, π₯π₯ = 0, and π₯π₯ = ππ, οΏ½ind
the volume of the solid generated by revolving the region about the π₯π₯-axis.
5. Find the volume of the solid generated by revolving the shaded
region about the indicated π¦π¦-axis.
6. Evaluate
1
οΏ½ π₯π₯ ln π₯π₯ ππππ
0
7. Evaluate
3π₯π₯ + 5
οΏ½
ππππ
(π₯π₯ − 1)2 (π₯π₯ + 2)
8. Evaluate
οΏ½ ππ π₯π₯ π₯π₯ 2 ππππ
9. Use two different methods to evaluate the following:
οΏ½ π₯π₯ οΏ½4 − π₯π₯ 2 ππππ
0
