# I Does an inverse Riemann exist?

Tags:
1. Apr 11, 2016

### smilodont

I already googled this but I did not find a definite answer. Is there such a thing as a 'inverse riemann'? Specifically, where you invert the start number to be at the top of the riemann symbol and then decrement down to the end value which is on the bottom of the riemann symbol?

2. Apr 11, 2016

### mathman

Thereis nothing special about the integral you described. Switching the end points simply means changing the sign of the integral.

3. Apr 11, 2016

### smilodont

Ok, explain what you mean. I had never seen that before.

4. Apr 11, 2016

### WWGD

Do you mean $g(x):= \int_a^x f(t)dt$ , where x is a variable?

5. Apr 12, 2016

### mathman

$\int_a^bf(x)dx=-\int_b^af(x)dx$

6. Apr 12, 2016

### zinq

Smilodont: The name "Riemann" is associated with so many concepts that it would help a lot if you spelled out what you mean in some detail.

7. Apr 12, 2016

### smilodont

∑ is a riemann. You pointed out an integral. They are similar but not the same. I am talking about the riemann sum. hope that clarifies.

8. Apr 13, 2016

### mathman

Riemann sum is used as approximation to Riemann integral. In that context what exactly is your question?

9. Apr 13, 2016

### smilodont

i am interested in the ∑ use. i was confused in calling it a riemann sum. too long since college. it's a summation symbol. what i was interested in is if you can put the higher value on the bottom and lower value on the top. If so, is that viewed as indicating you wish to decrement from the value at the top to the value at the bottom?

10. Apr 14, 2016

### Staff: Mentor

No, the symbol ∑ represents a sum or summation. As far as I know there is no such thing as "a riemann," short of being a reference to someone with that name.
A summation typically looks something like this:
$$\sum_{j = 1}^n a_j$$
The index starts at the value at the bottom and increases up through the upper value above the summation symbol. I've never seen a summation where the index was decremented, and I don't think there is any commonly used notation to indicate this.