-
Evaluating double integrals over general domains
The process of evaluating a double integral over a region in a plane is explained and illustrated with examples.
The solution is in a PDF file.
-
Double Integral Evaluated
Then
So
,
and it the whole circle,
In the polar coordinates,
So This provides an example of evaluating a double integral using polar coordinates.
-
Double Integral and Change of Order of Integration
33882 Double Integral and Change of Order of Integration I) Evaluate the integral....
ii) Change the order of integration and verify the answer is the same by evaluating the resulting integral.
-
Integral with an ellipse
174700 Ellipse integral See attached page for problem.
Use the given transformation to evaluate the integral. Please see the attached file. This shows an example of evaluating a double integral involving an ellipse.
-
Reverse order of integration
To change the integration order to integrate on y first, we have:
and
So the double integral is This provides an example of evaluating an integral by reversing order of integration.
-
Integral - change of variables
[int (0, 2) v dv]
= (1/3) (sec 1 + tan 1 - 1)(2) This provides an example of evaluating a double integral using change of variables.
-
Evaluate the indefinite integral of the transcendental function.
keywords: integration, integrates, integrals, integrating, double, triple, multiple
keywords : find, finding, calculating, calculate, determine, determining, verify, verifying, evaluate, evaluating, calculate, calculating, prove, proving Please see the
-
Indefinite Integrals : Partial Fractions
110078 Indefinite Integrals : Partial Fractions Use the method of partial fractions to evaluate the indefinite integral (Let u= ln[x])
(integral) (7+11*ln[x]^2)/(x*ln[x]^3+x*ln[x])
keywords: integration, integrates, integrals, integrating, double
-
Double integral with change of variables.
> g:=int(int(8*(3*u+v)^2,u=0..1-v),v=0..1); #Evaluating the integral after the change of variables
>
> g:=x^2;
> a:=int(int(g,y=x/3..3*x),x=0..1); #Evaluating the first integral
> b:=int(int(g,y=x/3..4-x),x=1..3)