integral numerically

[yumi382]

Hi! I need to calculate integral numerically using rectangle rule, trapezoidal rule and Simpson's rule. (for the points x = 0.2; 0.3; 0.4; 0.6; 0.9; 1.0).
Could someone explain it to make how to do it at least for 0.2? The rest I would try on my own. I've been reading about it and still have no idea...

 

[Deleted member 4993]

Hi! I need to calculate integral numerically using rectangle rule, trapezoidal rule and Simpson's rule. (for the points x = 0.2; 0.3; 0.4; 0.6; 0.9; 1.0).
Could someone explain it to make how to do it at least for 0.2? The rest I would try on my own. I've been reading about it and still have no idea...


View attachment 26657

Do you know the process of numerical integration?

 

[yumi382]

Not really, I have just started learning it. And I don't get it why there is t, dt etc. The tasks we did had dx..

 

[Deleted member 4993]

Not really, I have just started learning it. And I don't get it why there is t, dt etc. The tasks we did had dx..

Which textbook are you following in class?

Did you watch any video/s on this topic in the internet?

 

[nasi112]

This is a great video to explain Simpson's rule.

 

[Deleted member 4993]

Not really, I have just started learning it. And I don't get it why there is t, dt etc. The tasks we did had dx..

"x" or "t" are variables - just a name. So - if it makes you more comfortable, solve the following problem:

I need to calculate integral numerically using rectangle rule, trapezoidal rule and Simpson's rule. (for the points t = 0.2; 0.3; 0.4; 0.6; 0.9; 1.0).

The integral being:

` \int_0^t \sqrt{x} * sin(x) \ dx `

 

[Dr.Peterson]

Hi! I need to calculate integral numerically using rectangle rule, trapezoidal rule and Simpson's rule. (for the points x = 0.2; 0.3; 0.4; 0.6; 0.9; 1.0).
Could someone explain it to make how to do it at least for 0.2? The rest I would try on my own. I've been reading about it and still have no idea...


View attachment 26657

One thing that troubles me about this problem is that you aren't told what to use for n (that is, how many rectangles, etc, to use).

At first I read it as if the list of numbers were the points at which to divide the region, but they are clearly different values of the upper limit. Yet why would they make you repeat a (presumably manual) approximation process six times? You wouldn't be learning anything new the sixth time.

Can you show us an image of the entire problem, so we can be sure what it is asking of you? And have they previously told you (perhaps in the instructions for a group of problems) how many parts to use?