MA 242 Honors 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

á   Examples p. 836: 1,3,11

 

Section 12.2 Iterated Integrals:

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

á   Examples p.842: 3, 13, 19

 

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.850 33,39)

á   Know property 10 on p. 849

á   See 12.3 Worksheet

á   Examples p. 850: 13,17,23, 50

 

Section 12.4 Double Integrals in Polar Coordinates:

á   Know how to change from rectangular to polar coordinates

á   See 12.4 Worksheet

á   Examples p. 856: 4,8,9, 15,16,17,19,20,25,31

 

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: 3,7,14

 

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. 879: 11,13,19,39

 

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 685 and 687

 

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   See 12.7/12.8 Worksheet

á   Examples p. 887: 9,11,19,21,23,27,31,33

 

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