1a) Find the approximate value of ∫[0~1] e^[(x^2)/2] dx by using th trapezoidal rule with 5 sub-intervals.
b) Hence, finf the approximate value of ∫[-1~1] e^[(x^2)/2] dx.
For (b),
∫[-1~1] e^[(x^2)/2] dx
=∫[0~1] e^[(x^2)/2] dx + ∫[-1~0] e^[(x^2)/2] dx
The first no. is the answer of (a), but how should I calculate the second no.?
2) Approximate the area of the region bounded by the curve y=5/x and the line
x+y-6=0 by using the trapezoidal rule with 4 sub-intervals.
I want to ask how to define which one is right boundary and which one is left
boundary? Or how can the graph be drawn?
Please help, thank you!
F.5 maths m1 trapezoidal rule
2015-01-08 9:48 pm
回答 (2)
2015-01-10 6:33 am
✔ 最佳答案
--------------------------------------------------------------------------------------------圖片參考：https://s.yimg.com/rk/HA00482599/o/566340809.png
2015-01-08 10:15 pm
"I want to ask how to define which one is right boundary and which one is left
boundary?"
You need to solve for the intersections first.
{ x + y - 6 = 0
{ y = 5/x
to get
(x, y) = (1, 5) or (5, 1)
2015-01-08 14:17:47 補充：
For your part (a) enquiry, let y = -x and you can see that both integrals are the same.
This is the issue of integrating an even function from -a to a.
https://www.proofwiki.org/wiki/Definite_Integral_of_Even_Function
2015-01-08 15:50:47 補充：
You can roughly sketch the two lines and know that the straight line is above the curve between the two intersection points.
Then you can know the area is
∫[1 ~ 5] [(6 - x) - 5/x] dx
2015-01-08 15:52:09 補充：
If you read the formula, you can also know without sketching the graph that
(6 - x) is greater than 5/x for 1 < x < 5
Then you can know which to minus which inside the integral.
boundary?"
You need to solve for the intersections first.
{ x + y - 6 = 0
{ y = 5/x
to get
(x, y) = (1, 5) or (5, 1)
2015-01-08 14:17:47 補充：
For your part (a) enquiry, let y = -x and you can see that both integrals are the same.
This is the issue of integrating an even function from -a to a.
https://www.proofwiki.org/wiki/Definite_Integral_of_Even_Function
2015-01-08 15:50:47 補充：
You can roughly sketch the two lines and know that the straight line is above the curve between the two intersection points.
Then you can know the area is
∫[1 ~ 5] [(6 - x) - 5/x] dx
2015-01-08 15:52:09 補充：
If you read the formula, you can also know without sketching the graph that
(6 - x) is greater than 5/x for 1 < x < 5
Then you can know which to minus which inside the integral.
收錄日期: 2021-04-15 17:49:21
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20150108000051KK00036