The document introduces double integrals, Fubini's theorem, and their applications in calculus, highlighting properties and problem-solving techniques. It explains the significance of Fubini's theorem in changing the order of integration and its relevance in computing areas, volumes, and more. Additionally, it provides references for further study on double integrals.

1. Double Integral Over Rectangle, Fubinies
Theorem, Properties Of Double Integral.
Active Learning Assessment
Calculus(2110014)
Semester:1
Made by:- Burhanuddin Kapadia
Enrolment : 170120119026
Class: ME H2
Submitted to: Prof. Keyuri Shah

2. Content
• Introduction to double integral
• Introduction to double integral over rectangle
• Introduction to fubini’s theorem
• Problem solving
• Properties of double integral
• Application of double integral
• Reference

3. Introduction to Double Integral

4. Introduction to double integral over
rectangle
RR
d
c
a b
y
x

5. Introduction to Fubinis Theorem
• In mathematical analysis Fubini's theorem, named after Guido Fubini, is a result
which gives conditions under which it is possible to compute a double integral
using iterated integrals.
• As a consequence it allows the order of integration to be changed in iterated
integrals.
• There are two methods to evaluate double integral,

6. Fubinis Theorem
y
O x
P
S
x=a y=b
A
Q
R
B

7. Fubinis theorem
y
A
S
B
y=c
y=d R
QP
xO

8. Problem Solving

9. Problem Solving

10. Properties of double integral

11. Properties of double integral

12. Properties of double integral

13. Application Of double integral
• Double integrals arise in a number of areas of science and engineering, including
computations of
• Area of a 2D region
• Volume
• Mass of 2D plates
• Force on a 2D plate
• Average of a function
• Center of Mass and Moment of Inertia
• Surface Area

14. References
• https://
math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuid es/vcalc/255
• http://courses.washington.edu/trcalcii/QSci292/dbl_integ_read.pdf
• https://sites.math.washington.edu/~morrow/335_12/fubini.pdf
• http://www.math.usm.edu/lambers/mat280/spr10/lecture10.pdf
• https://www.math24.net/definition-properties-double-integrals/

15. Thank You