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Lecture

8.2 Surface Area of Revolution Question #5 (Medium)

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Department
Mathematics
Course
MAT136H1
Professor
All Professors
Semester
Winter

Description
8.2 Challenging Integral Applications Surface Area of Revolution Question #5 (Medium): Surface Area Approximation Using Simpson’s Rule Strategy Surface area is given by: ∫ √ ( ) Simpson’s rule states: ∫ ( ) [ ( ) ( ) ( ) ( ) ( ) ( ) ( )] , where is even and . Sample Question Using Simpson’s Rule with approximate the surface area obtained by rotating the function about the x-axis. Then compare the answer to the value from the calculator. ( ), Solution First, the integral expression needs to be established, which requires . Thus: . Plugging into the surface area formula: ∫ √ ( ) ∫ ( )√ ( ) ( ) ( √ ∫ ( ) √ ( ) ∫ ( ) . To apply Simpson’s rule, let ( ) ( √ [ ( )
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