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.

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Presentation transcript:

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.

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

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

Definite Integrals

Definite Integrals

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

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.

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

Area between curves

Volume Disk/ Washer method

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

Volume: shell method

Comparing methods

Arc length of curve

Area of a surface of revolution

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