Math 166 SI Session
Objectives
- Get to know each other! Get to know classmates and your SI leader!
- Super quick review on how to solve derivatives and integrals.
- What do integrals mean?
- How to find volume of solids using integrals.
- Visualizing & drawing solids
- Disk Method
Activities
Names & Introductions- (1 min) Introduce myself: name, year, major, San Diego story, no stupid questions
- (5min) Say name, major, fun question: If you were to make a hot chocolate stand, what (real or made up) street would you sell your hot chocolate on and why?
- (5 min) Do the activity again but in the groups. I’ll give you 3 minutes to learn everyone’s name in your group and put a face to it. I’ll call on each group and one person from each group must be able to say everyone’s name.
- Take the derivative of
- Write out steps to finding a derivative as a group
- Take the indefinite integral of what you just got
- Write out steps of finding an integral as a group
- How would the steps change if we were to have a definite integral?
- Write out what an integral means/ what does it do?
- What does dx mean?
- Find the volume of a solid with square cross sections that are perpendicular to the x axis whose diagonal goes from y= to y= The solid is bounded by two planes (that are perpendicular to the x axis at) x=0 and x=4. Find the volume.
- Draw out the picture
- Set up integral
- Solve it
- (5 min) Same problem but this time the cross sections are circles and the diameter goes from y= to y= Find the volume.
- Find the volume of a solid where the function y=2x is rotated around the x axis from x=0 to x=3.
- Draw the picture
- Draw a cross section and label
- Set up integral and solve
- What does each part of the integral mean? *hint: Look at your cross section labeling. What would your height be for that cross section?
What does dx mean? - Check: Volume of cone= base area * height
- Now rotate the curve around x=4 and the curve is bounded from x=4 to x=8.
- (10 min) Find the volume of a solid created by rotating the curve x= around the y axis from y=-2 and y=2.
- Draw the picture
- Draw a cross section and label
- Set up integral and solve
- Check: Volume of sphere =
- Answer any questions
- Give students a sheet of paper (name) (what you are looking to get out of SI) (activities you would like to see)
1/17/18
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