integrate with the upper limit is a function

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L.GREEN 2024-7-31

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移动：Star Strider 2024-8-4

Hello!

How to integrate a function on Matlab with the upper limit is a function, for exemple the following integral:

i tried this code:

U= vpa(int(f,s,0,t^2))

but it returns int(f,s,0,t^2)!!

is there any method to do it?

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Walter Roberson 2024-7-31

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If you have working with a mix of scalar constants and scalar symbolic variables, then you can use ^ and / instead of .^ and ./ . You only need .^ and ./ if you are working with non-scalar values.

syms s t

f1 = sin(0.008414709848078965066525023216303*exp(-2*s^(1/2)) + 0.00008414709848078965066525023216303*cos(s)^2 + 0.008414709848078965066525023216303) + 1

f1 =

f2 = sin(0.008414709848078965066525023216303*exp(-2*s.^(1/2)) + 0.00008414709848078965066525023216303*cos(s).^2 + 0.008414709848078965066525023216303) + 1

f2 =

isAlways(f1 == f2)

ans = logical

Torsten 2024-8-1

移动：Star Strider 2024-8-4

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The inconvient of the intergal function is that we need to use '.^ 'and/or './'

If you have a symbolic function and want to convert it to a function that can be used together with "integral", use "matlabFunction". Here, you will also get .^, ./ and .* operators.

Another way is to use the 'ArrayValues',true option for "integral" that passes one value for s to the function at a time. The disadvantage is that this option might slow down the integration:

f = @(s) sin(0.008414709848078965066525023216303*exp(-2*s^(1/2)) + 0.00008414709848078965066525023216303*cos(s)^2 + 0.008414709848078965066525023216303) + 1;

F = @(t) integral(f,0,t^2,'ArrayValued',1);

tnum = 0:0.1:5;

Fnum = arrayfun(@(t)F(t),tnum);

plot(tnum,Fnum)

grid on