Portfolio Problem 1

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School

University of Central Florida *

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Course

2312

Subject

Mathematics

Date

Feb 20, 2024

Type

docx

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Uploaded by yaelfaroud

Portfolio Problem 1 In the picture below, you will find a shaded region bounded between the curves 𝑦 = 4 𝑥 and y = x 3 . Set up and solve an integral to find the volume of the resulting solids described in the problems below. 1. Use the Shell Method to set-up and solve an integral to find the volume of the solid obtained by rotating the shaded region about the x - axis. Use the Fundamental Theorem of Calculus to solve the integral and use a fraction involving ‘pi’ in your final answer.

2. Use the Washer Method to set-up and solve an integral to find the volume of the solid obtained by rotating the shaded region about the horizontal line y = 8 . Use your calculator to compute the integral and use a fraction involving ‘pi’ in your final answer.

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Portfolio Problem 1

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