Quiz7s - 1 = 1 3 Observe that A is symmetric with respect...

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MATH 1501 Quiz 7 November 2, 2009 No books or notes allowed. No laptop, graphic calculator or wireless devices allowed. Write clearly. Name:
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MATH 1501 Quiz 7 November 2, 2009 1. (10 points) Given f ( x ) = x (1 - x ) let A be the finite region of the plane contained between - f ( x ) and f ( x ). That is A is defined by; 0 x 1 - x (1 - x ) y x (1 - x ) Find the area of A and the volume of the solid S obtained by rotating A around the y axis (use the symmetries of A to simplify the computations). Solution: The area of A is given by Area( A ) = 2 Z 1 0 x (1 - x ) dx = 2 ˆ x 2 2 1 0 - x 3 3
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Unformatted text preview: 1 ! = 1 3 . Observe that A is symmetric with respect to the x axis and the vertical line x = 1 / 2 so that the centroid of A is ¯ x-1 / 2 and ¯ y = 0. Form Pappus theorem it follows that Vol( S ) = 2 π ¯ x Area( A ) = π 3 . Without using Pappus Theorem, the volume can be computed with the shells method and is given by Vol( S ) = 4 π Z 1 x 2 (1-x ) dx = 4 π ˆ x 3 3 fl fl fl fl 1-x 4 4 fl fl fl fl 1 ! = π 3 . Page 1 of 1...
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This note was uploaded on 05/23/2010 for the course MATH 1501 taught by Professor N/a during the Fall '08 term at Georgia Tech.

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Quiz7s - 1 = 1 3 Observe that A is symmetric with respect...

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