Week 2 Multi-Variate Integration

Question 1

how does a multi-variate integral work

Answer 1

it is broken down into separate integrals from innermost to outermost

Question 2

what are the 4 limit statements for multi-variate integrals

Answer 2

1 - the limits can be numbers, constants or functions of variables
2 - the innermost can have limits involving functions of other variables
3 - the middle integrals can have limits involving only outer variables
4 - the outermost can only have limits that are numbers or constants

Question 3

what is the first step for solving a multivariate integral

Answer 3

draw a diagram

Question 4

what is the second step for solving a multivariate integral

Answer 4

identify the elemental

Question 5

what is the third step for solving a multivariate integral

Answer 5

find the limits

Question 6

what is the fourth step for solving a multivariate integral

Answer 6

decide the order to integrate (usually most complicated first)

Question 7

what are the fifth and sixth steps for solving a multivariate integral

Answer 7

5 check the limits

6 do the integral and check the answer

Question 8

when is it often more useful to use polar coords over cartesian

Answer 8

when there is symmetry

Question 9

what is the elemental circular area

Answer 9

dA = rdrdθ

Question 10

what is the elemental cylindrical volume

Answer 10

dV = rdrdθdz

Question 11

what is the elemental spherical volume

Answer 11

dV = r^2sinθdθdφ