MA 242 Test 3 Review Sheet (covers 12.1-12.5, 12.7,9.7,12.8)

 

Section 12.1 Double Integrals over Rectangles:

á   Know the definition of a double integral on p.831

 

Section 12.2 Iterated Integrals:

á   Be able to set up and evaluate double integrals over a rectangular region R

á   Examples p.843: 3, 17, 30

 

Section 12.3 Double Integrals over General Regions:

á   Be able to set up & integrate double integrals over a region D

á   Be able to find volumes using double integrals

á   Be able to sketch a region D and change the order of integration (p.852 41,45,47,49)

á   Know property 10 on p. 850

á   Examples p. 851: 19, 23, 29

 

Section 12.4 Double Integrals in Polar Coordinates:

á   Know how to change from rectangular to polar coordinates

á   Examples p. 857: 4,9, 11,15,20,27

 

Section 12.5 Applications of Double Integrals

á   Given a density function, be able to find the mass, moments, and center of mass of a lamina.

á   Examples p. 866: 3,7

 

Section 12.7 Triple Integrals:

á   Be able to set up and evaluate triple integrals, find volume using triple integrals, and find mass of a solid E given a density function.

á   Examples p. 881: 11-21 odd

 

Section 9.7 Cylindrical and Spherical Coordinates:

á   You need to know how to convert back and forth between rectangular and cylindrical coordinates and rectangular and spherical coordinates

á   Know the red boxes on pages 682 and 684

 

Section 12.8 Triple Integrals in Cylindrical and Spherical Coordinates

á   You will need to be able to set up and evaluate integrals in both cylindrical and spherical coordinates

á   Examples p. 887: 9,11,13,19,21,31

 

Other Helpful Information for the Test:

á   Equation and graph of a plane (p.670 box 8)

á   Equation and graph of a paraboloid, cone (p.682)

á   Equation and graph of a sphere (p.640)

á   Equation of a line

á   Equation and graph of a cylinder

á   Sin and Cos at basic angles (See the 2nd reference page at the very front of your book)

á   U-substitution

á   Integration by Parts