MATH 102 (Spring 24) • Final • Multivariable Calculus

Intuition: Double Integrals

Volume Calculation with Double Integration

Area Calculation with Double Integral

Sketching the Area of Integration 1

Sketching the Area of Integration 2

Sketching the Area of Integration 3

Reversing the Order of Integration 1

Reversing the Order of Integration 2

Reversing the Order of Integration 3

Reversing the Order of Integration 4

Sketching & Reversing the Integration Area

Cartesian to Polar Coordinates 1

Cartesian to Polar Coordinates 2

Polar to Cartesian Coordinates

Double Integrals in Polar Coordinates 1

Double Integrals in Polar Coordinates 2

Double Integrals in Polar Coordinates 3

Double Integrals in Polar Coordinates 4

Exam like Question 1

Exam like Question 2

Exam like Question 3

Exam like Question 4

Exam like Question 5

Exam like Question 6

Exam like Question 7

Exam like Question 8

Exam like Question 9

Exam like Question 10

Exam like Question 11

Exam like Question 12

Exam like Question 13

Exam like Question 14

Exam like Question 15

Exam like Question 16

Exam like Question 17

Exam like Question 18

Exam like Question 19

Exam like Question 20

Exam like Question 21

Reversing the Order of Integration 1

Reversing the Order of Integration 2

Reversing the Order of Integration 3

Reversing the Order of Integration 4

Reversing the Order of Integration 5

Double Integral 1

Double Integral 2

Area Between Curves in Polar Coordinates

Double Integral in Polar Coordinate 1

Double Integral in Polar Coordinate 2

Double Integral in Polar Coordinate 3

Double Integral in Polar Coordinate 4

Double Integral in Polar Coordinate 5

Double Integral in Polar Coordinate 6

Double Integral in Polar Coordinate 7

Double Integral in Polar Coordinate 8

Double Integral in Polar Coordinate 9

Double Integral in Polar Coordinate 10

Introduction to Triple Integrals

Triple Integrals 2

Triple Integrals 3

Important Functions and Their Graphs

Triple Integrals 4

Triple Integrals 5

Triple Integrals 6

Reversing the Order of Triple Integrals

Volume with Double or Triple Integral 1

Volume with Double or Triple Integral 2

Volume with Double or Triple Integral 3

Cylindrical Coordinates 1

Cylindrical Coordinates 2

Change of Variable in Triple Integrals

Change of Variable: Cartesian to Cylindrical

Triple Integral in Cylindrical Coordinates 1

Triple Integral in Cylindrical Coordinates 2

Triple Integral in Cylindrical Coordinates 3

Triple Integral in Cylindrical Coordinates 4

Triple Integral in Cylindrical Coordinates 5

Triple Integral in Cylindrical Coordinates 6

Spherical Coordinates 1

Spherical Coordinates 2

Change of Variable: Cartesian to Spherical

Triple Integral in Spherical Coordinates 1

Triple Integral in Spherical Coordinates 2

Triple Integral in Spherical Coordinates 3

Triple Integral in Spherical Coordinates 4

Triple Integral in Spherical Coordinates 5

Triple Integral in Spherical Coordinates 6

Triple Integral in Spherical Coordinates 7

Triple Integral in Spherical Coordinates 8

Choose your side 1: Spherical or Cylindrical

Choose your side 2 : Cylindrical or Spherical or Cartesian

Choose your side 3 : Cylindrical or Spherical or Cartesian

Choose your side 4 : Cylindrical or Spherical or Cartesian

Change of Variable - Double Integral

Triple Integral in Cylindrical Coordinates

Triple Integral in Cylindrical Coordinates

Double Integral & Triple Integral in Cylindrical Coordinates

Triple Integral in Spherical Coordinates

Triple Integral in Spherical Coordinates

Triple Integral in Spherical Coordinates

Triple Integral in Spherical Coordinates

Triple Integral in Cylindrical & Spherical Coordinates

Triple Integral in Cylindrical & Spherical Coordinates

Triple Integral in Cartesian & Cylindrical & Spherical Coordinates

Triple Integral in Cartesian & Cylindrical & Spherical Coordinates

Triple Integral in Cartesian & Cylindrical & Spherical Coordinates

Triple Integral in Cartesian & Cylindrical & Spherical Coordinates

Vector Functions and Curves

Domain of a Vector Function

Limit of a Vector Function

Derivative of a Vector Function

Integral of a Vector Function

Arc Length

Arc Length Parametrization

Line Integral 1

Line Integral 2

Line Integral 3

Line Integral 4

Line Integral 5

Vector Fields and Field Lines

Conservative Fields

Potential Function

Line Integrals of Vector Fields

Green's Theorem

Exam like Question 1

Exam like Question 2

Exam like Question 3

Exam like Question 4

Exam like Question 5

Exam like Question 6

Exam like Question 7

Exam like Question 8

Exam like Question 9

Exam like Question 10

Exam like Question 11

Exam like Question 12

Exam like Question 13

Exam like Question 14

Conservative Field & Potential 1

Conservative Field & Potential 2

Conservative Field & Potential 3

Conservative Field & Potential 4

Conservative Field & Potential 5

Conservative Field & Potential 6

Conservative Field & Line Integral

Line Integrals 1

Line Integrals 2

Line Integrals 3

Line Integral 4

Line Integral 5

Line Integrals of Vector Fields 1

Line Integrals of Vector Fields 2

Divergence and Curl

Green's Theorem 1

Green's Theorem 2

Green's Theorem 3

Green's Theorem 4