MATLAB: Where is the mistake

ezplotintegration

ezplot('int((x*x*normpdf(x,1,2)))',[-20 20 0 2])

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What is being integrated? What is the lower bound? What is the upper bound?

Your use of [-20 20 0 2] suggests that you are expecting to plot over two dimensions. As you have an integral, that would require three variables, with one of them being the variable of integration. Your expression only has one variable, and it would be used as the variable of integration if the integral worked, leaving you with two extra variables.

Remember that int() is strictly for symbolic integration.

syms x
f = int((x*x*normpdf(x,1,2)))
f = 
ezplot(f,[-20 20 0 2])

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MATLAB: Integration showing wrong answer

It is the correct result, although it may not be the one you were anticipaiting.

Try this:

syms x 
f(x) = sin(x)+2*cos(x)
intf = int(f)
simplifiedResult = simplify(intf, 'Steps', 100)

producing:

f(x) =
2*cos(x) + sin(x)
 
intf(x) =
-2*cos(x/2)*(cos(x/2) - 2*sin(x/2))
 
simplifiedResult(x) =
2*sin(x) - cos(x) - 1

MATLAB: Integral of exp(-x)*P(x)/Q(x) in terms of exponential integral in symbolic tooblox

What is the concern with the result that was returned? It looks like the SMT came back with the best answer it could with the information it was given. The form of the result would be a bit simpler by putting assumptions on 'a' if sensible to do so:

>> syms a positive
>> int(x*exp(-a*x)/(x^2+1),x,[0 inf])
 
ans =
 
(2*meijerG(1, [], [1, 1, 3/2], [], a^2/4))/(a^2*pi^(1/2))

But until a value is assigned to 'a' what shold the expected result be? Of course, the integral can be evaluated at a value of interest:

>> f(a)=int(x*exp(-a*x)/(x^2+1),x,[0 inf])
 
f(a) =
 
(2*meijerG(1, [], [1, 1, 3/2], [], a^2/4))/(a^2*pi^(1/2))
 
>> vpa(f(5))
 
ans =
 
0.033896

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Related Solutions

MATLAB: Integration showing wrong answer

MATLAB: Integral of exp(-x)*P(x)/Q(x) in terms of exponential integral in symbolic tooblox

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