- #1

- 1,009

- 0

Solution:

A = Lim ( ∏/(2n) * Ʃ cos( ∏i/(2n)) = ? Start: i = 0 and End: n = n

n → ∞

Just like there is a theorem for adding consecutive numbers... n(n + 1)/2..

Is there one for trig functions?

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- #1

- 1,009

- 0

Solution:

A = Lim ( ∏/(2n) * Ʃ cos( ∏i/(2n)) = ? Start: i = 0 and End: n = n

n → ∞

Just like there is a theorem for adding consecutive numbers... n(n + 1)/2..

Is there one for trig functions?

- #2

- 9,568

- 774

- #3

- 1,009

- 0

That is easy so I wanted to try and solve for n rectangles..

- #4

- 9,568

- 774

That is easy so I wanted to try and solve for n rectangles..

That's good that you found it so easy. That means you get the idea and that is what counts. There is a reason calculus books typically only do the limit thing for parabolas. Try that if for y = x

Trying it for most functions will leave you with a sum that you can't evaluate in closed form, such as you have just experienced. That is why the fundamental theorem of calculus is so important.

- #5

- 1,009

- 0

Estimate the area under the graph of f(x) = 1 + x^2 from x = -1 to x = 2 using 6 rectangles and right end point.

Question:

Can I change the equation from 1 + x^2 to 1 + (x - 1)^2 and change the interval to x = 0 to x = 3 ??

This seems logical because technically it would be the same area.. and it is easier for me to break up into 6 rectangles.

- #6

Science Advisor

Homework Helper

- 26,259

- 622

Just for the record, there are formulas like that. See http://en.wikipedia.org/wiki/List_of_trigonometric_identities Look under "Other sums of trigonometric functions". You can derive them by summing the geometric series exp(i*a*k) and splitting into real and imaginary parts.

- #7

- 9,568

- 774

Estimate the area under the graph of f(x) = 1 + x^2 from x = -1 to x = 2 using 6 rectangles and right end point.

Question:

Can I change the equation from 1 + x^2 to 1 + (x - 1)^2 and change the interval to x = 0 to x = 3 ??

This seems logical because technically it would be the same area.. and it is easier for me to break up into 6 rectangles.

Yes you could, but I don't see why it is any easier.

Share:

- Replies
- 5

- Views
- 509

- Replies
- 6

- Views
- 474

- Replies
- 7

- Views
- 318

- Replies
- 9

- Views
- 130

- Replies
- 7

- Views
- 728

- Replies
- 15

- Views
- 976

- Replies
- 10

- Views
- 221

- Replies
- 1

- Views
- 432

- Replies
- 10

- Views
- 514

- Replies
- 1

- Views
- 385