Thread: Write a Riemann sum as an integral

1. Write a Riemann sum as an integral

I am given this problem in my calculus textbook, and the answer is B. I, however, would like to know why the answer is B.

My first guess was that it would be E because the interval is from 0 to 20, but when I think of it, I'm pretty sure it's not.

2. Originally Posted by pocketasian
I am given this problem in my calculus textbook, and the answer is B. I, however, would like to know why the answer is B.

My first guess was that it would be E because the interval is from 0 to 20, but when I think of it, I'm pretty sure it's not.

you are thinking of $\frac 1{20} \sum_{x = 1}^{20} \sqrt{\frac x{20}}$

don't mix up the summation with the integral.

now, i have a challenge for you. lets say i asked you to approximate $\int_0^{20} \!\!\! \sqrt x ~dx$ using right hand endpoints and 20 subintervals. what would your answer look like?

3. We started integrals in class recently, and I'm still trying to get a firmer grasp on the concept... So I'm probably wrong in general.

If I'm doing this correctly, I would approximate it to be about 61.666 with 20 subintervals using RRAM. Is this correct? So then what?

4. Originally Posted by pocketasian
We started integrals in class recently, and I'm still trying to get a firmer grasp on the concept... So I'm probably wrong in general.

If I'm doing this correctly, I would approximate it to be about 61.666 with 20 subintervals using RRAM. Is this correct? So then what?
no, i mean, form the Riemann sum, that is find your $\delta x$ and all that and plug it into the expression.

5. Would it be .6894?

6. Originally Posted by pocketasian
Would it be .6894?
sigh. coming up with a decimal approximation won't help. the point is to have you come up with the Riemann sum so that you can see why (B) is the answer to your problem.

7. Well then... I just don't get it. I apologize for my lack of understanding. Will you clarify and explain this to me, if it's not too much of a hassle? Thanks.

8. Oh wait, actually, I think I understand it now... I drew out a picture, and I see that the width of each subinterval is 1/20. And since there are 20 subintervals, B is the right answer because the integral is from 0 to 1.

Is this correct? If not, then I really don't know what I'm doing...

9. Originally Posted by pocketasian
Oh wait, actually, I think I understand it now... I drew out a picture, and I see that the width of each subinterval is 1/20. And since there are 20 subintervals, B is the right answer because the integral is from 0 to 1.

Is this correct? If not, then I really don't know what I'm doing...
yes, and had you written out the sum you would see that it is the same expression that you were asked about. you can try writing out the sums for the others to see what the differences are so you can learn to "see" it easier