Math380_Summer08_Exam3 - Name: Math 380 Exam 3 July 30,...

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

View Full Document Right Arrow Icon
Name: Math 380 – Exam 3 July 30, 2008 50 points possible 1. (a) (3pts) State the conclusion to the Change of Variables Theorem for Double Integrals and explain the role of the Jacobian factor in the integrand. (b) (7pts) Determine an appropriate change of variables and evaluate the integral ZZ R e x - y x + y dA where R is the rectangle bounded by the lines y = x , y = x + 5, y = 2 - x and y = 4 - x . (More space on following page if needed.) 1. (b) Continued. 2. Consider the change of variables T ( u,v,w ) = ( u 2 + 8 uw, v, u 2 w + 3 ) . Let D * be the set of ( u,v,w ) [ - 1 , 1] × [0 , 2] × [ - 1 , 0]. (a) (2pts) Find the Jacobian of T . (b) (2pts) Are there any points in D * where this change of variables may not be appropri- ate? Briefly explain. (c) (2pts) If f ( u,v,w ) is continuous on D * and f ( T ( u,v,w )) is continuous on D = T ( D * ), explain why this change of variables is still valid and the integral will evaluate correctly. 3.
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

Math380_Summer08_Exam3 - Name: Math 380 Exam 3 July 30,...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online