# Integral with only one limit of integration?

1. Homework Statement
Work it out with pencil and paper.
$$\int^x \frac{x'dx'}{1+x'^2}$$

2. Homework Equations
none

3. The Attempt at a Solution
My only question is what does it mean to have only one limit of integration? I am used to doing integrals in the indefinite case with no limits of integration, or in the definite case with two limits of integration.

What does this single limit of integration mean, and what do I do with it? Do I assume 0 for the other limit? Do I just solve it as a an indefinite integral?

Thanks for any clues!

1. Homework Statement

2. Homework Equations

3. The Attempt at a Solution

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## Answers and Replies

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cristo
Staff Emeritus
Science Advisor
I've never seen that notation before! I'd say you just integrate it indefinitely, then substitute x in for x'.

Yeah, I'd say set the bottom limit equal to 0 so that it makes the second part of the solution disappear.

HallsofIvy
Science Advisor
Homework Helper
The notation $\int^x f(x')dx'$ is just an indefinite integral. Remember that the variable inside the integral is a "dummy" variable- the "x" as a limit of integration just tells you what variable to use in the resulting function.

Do NOT set the bottom limit to 0! That is not justified.