Is My Reimann Sum Solution Correct for 6/(1+2x) from 0 to 2 with 4 Subintervals?

[Qube]

Homework Statement

Approximate the value of the integral of 6/(1+2x) with respect to x from 0 to 2. Use 4 subintervals of equal width and use the left endpoints.

Homework Equations

delta x = (b-a)/N

The Attempt at a Solution

The integral is the sum of 6/(1+i) from i = 0 to i = N-1 or 3 all multiplied by delta x, or 1/2.

This yields:

(1/2)(6 + 3 + 2 + (6/4))

= 3 + 3/2 + 1 + 3/4 = 4 + 1.5 + 0.75 = 5.5 + 0.75 = 6.25 = 25/4.

1) This is correct without the N term in the sum, right? I'm wondering because usually I have to take the limit as N approaches infinity but the N doesn't exist here, since N has already been defined.

2) Also is my work correct in general? I'm still getting a hang of this Reimann sum notation with the indices and n subintervals and the x star notation. I'll have to learn Latex another day!

 

[Dick]

Homework Statement

Approximate the value of the integral of 6/(1+2x) with respect to x from 0 to 2. Use 4 subintervals of equal width and use the left endpoints.

Homework Equations

delta x = (b-a)/N

The Attempt at a Solution

The integral is the sum of 6/(1+i) from i = 0 to i = N-1 or 3 all multiplied by delta x, or 1/2.

This yields:

(1/2)(6 + 3 + 2 + (6/4))

= 3 + 3/2 + 1 + 3/4 = 4 + 1.5 + 0.75 = 5.5 + 0.75 = 6.25 = 25/4.

1) This is correct without the N term in the sum, right? I'm wondering because usually I have to take the limit as N approaches infinity but the N doesn't exist here, since N has already been defined.

2) Also is my work correct in general? I'm still getting a hang of this Reimann sum notation with the indices and n subintervals and the x star notation. I'll have to learn Latex another day!

Yes, it's fine. And your work is fine in general. I don't know why you are asking all of these questions. As far as Riemann sums go, you can do a left sum, in which case i=N doesn't appear or a right sum in which case i=0 doesn't appear. These finite sums are just approximations to the true integral which you get by taking N->infinity. In which case it shouldn't matter whether it's left or right or something else.

 

[Qube]

Thanks again! Well, you guys helped me get a perfect score on my last chem test when the average was a 68% and the historic average was in the 50s. I got help here for free while my friends paid for help and still did dismally, or completely failed. I just want to make sure I'm right because I'd like to have a repeat performance on my calculus test! On the last calc test I actually scored over a 100 while the average was in the 70s, thanks again to PF.

Physics Forum is a grade saver! Thanks again to everyone who helped me and keeps helping me :)!

 

[Dick]

Thanks again! Well, you guys helped me get a perfect score on my last chem test when the average was a 68% and the historic average was in the 50s. I got help here for free while my friends paid for help and still did dismally, or completely failed. I just want to make sure I'm right because I'd like to have a repeat performance on my calculus test! On the last calc test I actually scored over a 100 while the average was in the 70s, thanks again to PF.

Physics Forum is a grade saver! Thanks again to everyone who helped me and keeps helping me :)!

Scoring over 100% is certainly worth a mention. At this point you should be getting a little more confident. Congratulations!