the expression 1/50 (1/50 +2/50+ 3/50+ .....50/50)is a Reimann sum approximation for

(everything in the parantheses is square root except the 1/50 outside the paratheses)

the answer has to me the integral form so from looking at the formula in my book i got:

1/50 * integral(from 0 to 50) square root x dx

hopefully i wrote the expression right in words correctly. tell me if it is confusing and i write it in different words .

My only concern with this answer is why is it from 0 to 50 isnt 50/50 1 not 50. That is my only discrepancy with your solution. so woulnt it be form 0 to 1? Im just asking

for clarification.

Yes, you are correct. The expression should be 1/50 * integral(from 0 to 1) square root x dx.

The expression you provided can be interpreted as a Riemann sum approximation for the integral. Let's go through the steps to clarify:

We have the expression: 1/50 (1/50 + 2/50 + 3/50 + ... + 50/50)

This can be written as: 1/50 * (1/50 + 2/50 + 3/50 + ... + 50/50)

Now, let's express the terms within the parentheses in terms of x:

1/50 * (sqrt(1/50) + sqrt(2/50) + sqrt(3/50) + ... + sqrt(50/50))

Simplifying the expression inside the parentheses:

1/50 * (sqrt(1)/sqrt(50) + sqrt(2)/sqrt(50) + sqrt(3)/sqrt(50) + ... + sqrt(50)/sqrt(50))

Now, we can rewrite this expression in integral form. The integral of the square root of x is ∫√x dx.

Let's substitute:

1/50 * (sqrt(1)/sqrt(50) + sqrt(2)/sqrt(50) + sqrt(3)/sqrt(50) + ... + sqrt(50)/sqrt(50))
= (1/50) * (√1/√50 + √2/√50 + √3/√50 + ... + √50/√50)

= (1/50) * (√1/√50 + √2/√50 + √3/√50 + ... + √50/√50)
= (1/50) * (√1/√50 + √2/√50 + √3/√50 + ... + √50/√50)
= (1/50) * ∫(√1 + √2 + √3 + ... + √50) dx

Now, let's consider the limits of integration. Since the expression is summing terms up to 50, it is appropriate to integrate from 0 to 50.

Therefore, we can rewrite the expression as:

(1/50) * ∫(√1 + √2 + √3 + ... + √50) dx, integrated from 0 to 50.

I hope this clarifies the steps for you. If you still have any questions, feel free to ask!

From your explanation, it seems that you have correctly identified the Riemann sum approximation and the integral form. However, there seems to be a misunderstanding regarding the limits of integration.

Let's break down the expression step by step to clarify:

1. The expression you provided is: 1/50 (1/50 + 2/50 + 3/50 + ... + 50/50).
This can be simplified as: 1/50 * (sum of (n/50) from n = 1 to 50).

2. Recognizing that the sum of (n/50) from n = 1 to 50 is simply the sum of the integers from 1 to 50 divided by 50, we get:
1/50 * (1/50 + 2/50 + 3/50 + ... + 50/50) = 1/50 * (1 + 2 + 3 + ... + 50)/50.

3. Simplifying further, we have: 1/50 * (sum of integers from 1 to 50)/50.
The sum of integers from 1 to 50 can be calculated as (50 * 51) / 2 = 1275.
Therefore, the expression becomes: 1/50 * 1275/50.

4. Now, addressing your concern about the limits of integration:
The integral form of the expression should have the limits corresponding to the range of the sum, which is from 1 to 50.
Hence, the integral should be from 1 to 50, not 0 to 50.

To summarize, the expression 1/50 (1/50 + 2/50 + 3/50 + ... + 50/50) can be written as the integral:

∫(1/50)√(x) dx, with the limits of integration being from 1 to 50.