{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

This preview shows pages 1–2. Sign up to view the full content.

MATH 1501 Quiz 7 November 2, 2009 No books or notes allowed. No laptop, graphic calculator or wireless devices allowed. Write clearly. Name:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 fl fl fl fl 1 0 - x 3 3 fl fl
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}