integral di e^(ax^3+bx) Dopo aver trovato l'integrale fare il Sviluppo di Taylor secondo grado X =0

integral di e^(ax^3+bx)

Dopo aver trovato l'integrale fare il Sviluppo di Taylor secondo grado X =0

[Dyuman Joshi]

Since this seems to be a HW question, show us what you have done.

Answer 1

[Infinite_king]

Hi LOIC CABREL,

Risponderò alla domanda in inglese. Utilizza Google Translate per tradurre la risposta nella tua lingua locale.

In MATLAB, you can create a symbolic expression and by using 'int' function you can find out the integral of the symbolic expression.

% creating a symbolic expression.
syms a x
f = a*x^2

f = 

% integrating the function.
int(f)

ans = 

For more information about integration, refer the following MATLAB resources

• Integration guide - https://www.mathworks.com/help/symbolic/integration.html
• Integration function - https://www.mathworks.com/help/symbolic/integration.html
• Symbolic expressions - https://www.mathworks.com/help/symbolic/create-symbolic-numbers-variables-and-expressions.html

Similarly, 'taylor' function can be used to calculate the taylor series expansion of the given function.

% creating the symbolic function
syms a b x
f = exp( a * x^3 + b *x)

f = 

% calculating taylor series expansion
ts = taylor(f,x,0,'order',3)

ts = 

For more information, refer the following documentation, https://www.mathworks.com/help/symbolic/sym.taylor.html

In some cases, the 'int' function cannot calculate the integral of the given function. This is because of any one of the following reasons,

• The antiderivative, F, may not exist in closed form.
• The antiderivative may define an unfamiliar function.
• The antiderivative may exist, but the software can't find it.
• The software could find the antiderivative on a larger computer, but runs out of time or memory on the available machine.

In these cases, one way to approximate the integral is by using the Taylor series to approximate the function and then calculating the integral of this approximate function. ( approximation around some point )

% creating the symbolic function
syms a b x
f = exp( a * x^3 + b *x)

f = 

% calculating taylor series expansion
ts = taylor(f,x,0)

ts = 

% calculating the antiderivative
int(ts)

ans =