This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 182 Homework Section 6.1 Problem 10 Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y . Draw a typical rectangle and then find the total area of the region. Region bounded by y = x 2 and y = 4 x x 2 The curves intersect when x 2 = 4 x x 2 2 x 2 4 x = 0 2 x ( x 2) = 0 x = 0 or x = 2 When x = 0 we have that y = 0 2 = 4  2 = 0 and when x = 2 it follows that y = 2 2 = 4 2 2 2 = 4 so the points of intersection are (0 , 0) and (2 , 4) as shown below: The width of the infinitely thin rectangles is dx and their height is the difference in y coordinates given by y down parabola y up parabola = 4 x x 2 x 2 = 4 x 2 x 2 . Therefore, the total area is integraldisplay 2 (4 x 2 x 2 ) dx = bracketleftbigg 2 x 2 2 3 x 3 bracketrightbigg  x =2 x =0 = 2 2 2 2 3 2 3 (0 2 2 3 3 ) = 8 16 3 = 24 16 3 = 8 3 Problem 16 Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y .....
View
Full
Document
This note was uploaded on 09/21/2009 for the course MATH 182 taught by Professor Keppelmann during the Spring '08 term at Nevada.
 Spring '08
 Keppelmann
 Math

Click to edit the document details