integral

can I able to integrate a function with some limits a, b but without define the values to the limit , e.g f(x) = x^3 -3*x , having limits x1, x2 but I don't want to assign the values to it . can I integrate it in Matlab

Answer 1

[Walter Roberson]

If you have the symbolic toolbox you can use int()

[Nasir Qazi]

can you solve the above example just to have an idea , I knw about syms but don't know, we can use it for limit integrals

Answer 2

[bym]

syms x a b
>> f = x^3-3*x;

>> int(f,a,b)

ans =

-((a + b)*(a - b)*(a^2 + b^2 - 6))/4

[Nasir Qazi]

what about this equation

cp = cp0 + b(T-T0), where T0 is lower limit and T is upper and 'cp0' and 'b' are constants , integration is done with respect to 'T'

[Walter Roberson]

Use the same method, changing the variable names as appropriate

syms T T0

cp = cp0 + b(T-T0)

int(cp, T, T0, T)

[Nasir Qazi]

is that right answer

((T - T0)*(2*cp0 + T*b - T0*b))/2

[Nasir Qazi]

% similarly here the answer is wrong

syms H R T a b

f = int((H/R*T^2),T,a,b)

f =

-(H*(a^3 - b^3))/(3*R)

% where 'H' , 'R', are constants and 'a', 'b' are limits and integrate it with respect to 'T' which on hands calculation is different and here it is wrong , why ?

[Walter Roberson]

That integral for f is certainly correct, as can be seen by removing the constant and realizing one is really only dealing with the integral of T^2, which of course yields 1/3*T^3

((T - T0)*(2*cp0 + T*b - T0*b))/2 is correct for the integral of cp with respect to T over T0 to T, but only provided that b(T-T0) is interpreted as meaning b*(T-T0) rather than b indexed at T-T0.