Understanding Integration in MATLAB: A Case Study

[furkang]

I used MATLAB to calculate the integration of a basic function.
I wrote :

F = inline('(2*x)+((x.^3)/0.000441)')

Q = quad(F,0.01,0.05)

I want to calculate integral of F from 0.01 to 0.05
the answer shown is 0.059
but the real answer is 0.361

I am sure the function F is correct (I have tried some values).

is there any problem with "Q = quad(F,0.01,0.05)" command?
Thank you for your help...

 

[gerben]

Why do you think the real answer is 0.361?
I see that
F(0.05) - F(0.01) = 0.361
but this is of course not the integral, the integral is smaller.

The function is increasing and so on the interval [0.01, 0.05] it is maximum at 0.05, there it is 0.3834. Overestimating the integral by assuming that F would be 0.3834 everywhere in the interval [0.01, 0.05] would give an area: 0.3834 * 0.04 = 0.0153
which is close to 0.0059 (the answer that quad gives).
I think 0.0059 is the right answer.

 

[furkang]

Why do you think the real answer is 0.361?
I see that
F(0.05) - F(0.01) = 0.361
but this is of course not the integral, the integral is smaller.

The function is increasing and so on the interval [0.01, 0.05] it is maximum at 0.05, there it is 0.3834. Overestimating the integral by assuming that F would be 0.3834 everywhere in the interval [0.01, 0.05] would give an area: 0.3834 * 0.04 = 0.0153
which is close to 0.0059 (the answer that quad gives).
I think 0.0059 is the right answer.

ok now 1ve got it , 1 made a big mistake but 1 am happy to know my command is true . Thank you again