1. Warm up
Find the area of surface formed by revolving the graph of f(x) = 6x3 on the interval [0, 4] about the x-axis.

2. Find the area of the surface formed by revolving the graph of f(x) = x2 on the interval [0, 4] about the y-axis.

3. The powerful Calculator
The calculator will…
Find the slope of a graph at a point
Not find the derivative
Find the area under a curve
Not find the Antiderivative

4. Definite Integrals

5. Definite Integrals

6. Definite Integrals
Keep in mind that area below x-axis is counted as negative.

9. How I will grade your work?
Must show definite integral completely!!! Most points will come from definite integral being found correctly. Some points will come from evaluating definite integral, if you show your work you are guaranteed partial credit, if you do it all in your calculator no partial credit if incorrect answer.

10. Review of topics Disk method Washer method Shell method
Area under curve
Volume
Disk method
Washer method
Shell method
Known cross sections
Arc length
Surface Area

11. Area between curves

12. Volume Disk/ Washer method

13. Solids with known cross sections
Area of square A = x2
Area of circle A = π r2
Area of equilateral triangle

14. Volume: shell method

15. Comparing methods

16. Arc length of curve

17. Area of a surface of revolution

18. In class practice Work together to complete the review page.
What you don’t finish becomes homework