17173

HP 32sII Manual

338
Zoom out
Zoom in
Previous page
1/376
Next page
D–8 More about Integration
File name 32sii-Manual-E-0424
Printed Date : 2003/4/24 Size : 17.7 x 25.2 cm
and you suspect that it may cause problems, you can quickly plot a few points
by evaluating the function using the equation or program you wrote for that
purpose.
If, for any reason, after obtaining an approximation to an integral, you
suspect its validity, there's a simple procedure to verify it: subdivide the
interval of integration into two or more adjacent subintervals, integrate the
function over each subinterval, then add the resulting approximations. This
causes the function to be sampled at a brand new set of sample points,
thereby more likely revealing any previously hidden spikes. If the initial
approximation was valid, it will equal the sum of the approximations over the
subintervals.
Conditions That Prolong Calculation Time
In the preceding example, the algorithm gave an incorrect answer because it
never detected the spike in the function. This happened because the variation
in the function was too quick relative to the width of the interval of integration.
If the width of the interval were smaller, you would get the correct answer; but
it would take a very long time if the interval were still too wide.
Consider an integral where the interval of integration is wide enough to
require excessive calculation time, but not so wide that it would be calculated
incorrectly. Note that because f(x) = xe
–x
approaches zero very quickly as x
approaches
∞
, the contribution to the integral of the function at large values
of x is negligible. Therefore, you can evaluate the integral by replacing
∞
,
the upper limit of integration, by a number not so large as 10
499
— say 10
3
.
Rerun the previous integration problem with this new limit of integration:
Keys: Display: Description:
0
`
3

_
New upper limit.
{
G
%º%1.%2
Selects Equation mode; displays
the equation.
{
)
X
!!
∫
/)
Integral. (The calculation takes a
minute or two.)
… 338 …


Need help? Post your question in this forum.

Forumrules


Report abuse

Libble takes abuse of its services very seriously. We're committed to dealing with such abuse according to the laws in your country of residence. When you submit a report, we'll investigate it and take the appropriate action. We'll get back to you only if we require additional details or have more information to share.

Product:

For example, Anti-Semitic content, racist content, or material that could result in a violent physical act.

For example, a credit card number, a personal identification number, or an unlisted home address. Note that email addresses and full names are not considered private information.

Forumrules

To achieve meaningful questions, we apply the following rules:

Register

Register getting emails for HP 32sII at:


You will receive an email to register for one or both of the options.


Get your user manual by e-mail

Enter your email address to receive the manual of HP 32sII in the language / languages: English as an attachment in your email.

The manual is 2,48 mb in size.

 

You will receive the manual in your email within minutes. If you have not received an email, then probably have entered the wrong email address or your mailbox is too full. In addition, it may be that your ISP may have a maximum size for emails to receive.

The manual is sent by email. Check your email

If you have not received an email with the manual within fifteen minutes, it may be that you have a entered a wrong email address or that your ISP has set a maximum size to receive email that is smaller than the size of the manual.

The email address you have provided is not correct.

Please check the email address and correct it.

Your question is posted on this page

Would you like to receive an email when new answers and questions are posted? Please enter your email address.



Info