Evaluating a double integral and demonstrating Fubini's Theorem with MATLAB
In the last video we quickly go through the nuts and bolts of evaluating this algebraically, comparing it to what we had in CP3D, and here we'll evaluated the integral with MATLAB and use MATLAB to demonstrate Fubini's Theorem
First we define our x and y symbolic variables
syms x y
Then we define our function
f(x,y)=24-x^2-3*y^2;
And now we use the integrate command nested within another integrate command,
So our inner integral is wrt y between 0 and 2
And our outer integral is wrt x between 0 and 3
int(int(f,y,[0 2]),x,[0 3])
And there we have our answer of 23 confirmed
Finally, we can also compare this to our Reimann sum from CP3D
And if we go back to that and ratchet up our increments in the x and y directions we see that our Reimann sum gets pretty close to 102, further confirming our answer.
But one final question here, what if we switch around the order of integration, will that give us a different answer?
Well, I would encourage you to do just using the calculus steps above, but since hopefully you trust MATLAB now that we’ve confirmed our answer, let’s try it there..
And… we see this does in fact give us the same answer,
This illustrates ‘Fubini’s Theorem’
So we can freely switch our order of integration as long as we keep the bounds consistent and as long as those bounds are just numbers. In the next video, we’ll discuss what happens when those bounds are actually functions rather than numbers, but until then, take care
-
4:55
JokoEngineering
10 years agoHow to Evaluate Improper Integrals Easier Method
4 -
1:23:46
DrOfEng
9 months agoIntegration and Accumulation of Change, Fast Revision, Worked Examples - Unit 6 - AP Calculus BC
1261 -
3:33
ProfEmersonAlves
1 year agoComprimento de arco por integral | Questão 50 de Cristalina -QUADRIX- Para se calcular o comprimento
2 -
6:15
ericntunctu
2 years agoCan you solve the following integral? integral of 1/(1+x^phi)^phi from 0 to infty
6 -
9:33
ericntunctu
2 years agoIntegral of 1/(x^3+1) step by step
1 -
17:01
kpmooney
3 years agoThe Trapezoid Rule: Estimating the value of a definite integral (using Python and Excel)
16 -
5:10
Mr. Antonucci Math
3 years agoHow to Evaluate a Definite Integral x^2-1 from x=1 to x=2 [Worked Example] Calculus
641 -
2:34:10
Prof Theago
2 years ago(EP07) INTEGRAL DO ZERO | INTEGRAL POR PARTES | TERÇA DO CÁLCULO @Professor Theago
2 -
0:24
Small Universe
1 year agoSolving Gaussian Integral in Seconds
6 -
7:25
ericntunctu
2 years agoTwo ways: Integral of 1/(x^2+1)^2 from 0 to infinity
1