orick3 - sphere of radius 2 centered at (0, 0, 2) which...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
MATH 22 Exam 3 Name: ______________________ FALL, 2000 1. (12 pts.) Evaluate the iterated integrals (a) x + x sin( y ) [ ] dy dx 0 p 1 4 (b) 1 - x 3 dx dy y 1 0 1 2. (14 pts.) The lamina D is enclosed the portion of the circle x 2 + (y – 2) 2 = 4 lying above the line y = 2 and has density given by r ( x , y ) = 2 sin 2 ( x 2 + y 2 ). Set up the integral expressions necessary to determine x and I x . It is not necessary to evaluate the resulting integrals. 3. (16 pts.) The volume of a solid region E is given by the triple integral dz dy dx 0 1 - y x 1 0 1 . Sketch the solid region E and write three other equivalent integral expressions for the volume (by interchanging the order of integration). It is not necessary to evaluate the integrals. 4. (14 pts.) Evaluate the integral dV E ∫∫∫ where E is the region enclosed in the
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: sphere of radius 2 centered at (0, 0, 2) which lies outside of the sphere of radius 3 centered at the origin. 5. (15 pts.) Find the area of the region enclosed in one leaf of the rose r = 2 cos2 q and which lies outside of the circle of radius 1 centered at the origin. 6. (15 pts.) Set up an integral expression for the surface area of z = 2 + ( xy ) 2 inside the cylinder ( x + 1) 2 + y 2 = 1. Express the integral in terms of polar coordinates. It is not necessary to evaluate the resulting integral. 7. (14 pts.) Use the transformation x = 3u + 2v, y = 2u 3v to evaluate ( x + 3 y ) dA R where R is the square bounded by the points (0, 0), (5, -1), (3, 2), and (2, -3). HINT: Take S = {(u, v) | 0 = u = 1; 0 = v = 1}...
View Full Document

This note was uploaded on 01/24/2011 for the course MATH 22 taught by Professor Brigham during the Winter '08 term at Missouri S&T.

Ask a homework question - tutors are online