Integral with only one limit of integration?

In summary, the notation \int^x f(x')dx' is an indefinite integral with x as a "dummy" variable. The variable inside the integral is just a placeholder for the resulting function. It is not justified to set the bottom limit to 0 in this case.
  • #1
DieCommie
157
0

Homework Statement


Work it out with pencil and paper.
[tex] \int^x \frac{x'dx'}{1+x'^2} [/tex]


Homework Equations


none


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!


 
Last edited:
Physics news on Phys.org
  • #2
I've never seen that notation before! I'd say you just integrate it indefinitely, then substitute x in for x'.
 
  • #3
Yeah, I'd say set the bottom limit equal to 0 so that it makes the second part of the solution disappear.
 
  • #4
The notation [itex]\int^x f(x')dx'[/itex] 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.
 

1. What is an integral with only one limit of integration?

An integral with only one limit of integration is a type of definite integral where the upper or lower limit of integration is missing. This means that the integral will be evaluated from a single point to either positive or negative infinity.

2. How do you solve an integral with only one limit of integration?

To solve an integral with only one limit of integration, you first need to identify the function being integrated. Then, you can use techniques such as substitution or integration by parts to evaluate the integral. In some cases, the integral may not be solvable with traditional methods and may require advanced techniques like contour integration.

3. What is the significance of an integral with only one limit of integration?

An integral with only one limit of integration is often used in physics and engineering to calculate quantities such as work, energy, and fluid flow rates. It can also be used to find the area under a curve or the volume of a solid of revolution.

4. Can an integral with only one limit of integration have a negative value?

Yes, an integral with only one limit of integration can have a negative value. This occurs when the function being integrated is negative over the interval of integration. In this case, the integral represents the signed area under the curve, which can be positive or negative depending on the function.

5. How is an integral with only one limit of integration related to the Fundamental Theorem of Calculus?

The Fundamental Theorem of Calculus states that the definite integral of a function can be evaluated by finding an antiderivative and evaluating it at the limits of integration. An integral with only one limit of integration follows this principle, but the missing limit of integration results in an indefinite integral that must be evaluated using other methods.

Similar threads

Two ways of integration giving different results
    • Calculus and Beyond Homework Help
Replies
9
Views
858
Integral Calculation: Compute l/sqrt(x2+l2)
    • Calculus and Beyond Homework Help
Replies
5
Views
791
Question re: Limits of Integration in Cylindrical Shell Equation
    • Calculus and Beyond Homework Help
Replies
24
Views
2K
A question about definite integrals and series limits
    • Calculus and Beyond Homework Help
Replies
12
Views
1K
Determine limits of integration in double integral change of variables
    • Calculus and Beyond Homework Help
Replies
2
Views
148
Jacobian: how to change limits of integration?
    • Calculus and Beyond Homework Help
Replies
16
Views
1K
How do I change this integral limit from x to t?
    • Calculus and Beyond Homework Help
Replies
2
Views
891
Solve ##\int\frac{e^{-x}}{x^2}dx## and ##\int \frac{e^{-x}}{x}dx##
    • Calculus and Beyond Homework Help
Replies
7
Views
701
Definite integral using only properties
    • Calculus and Beyond Homework Help
Replies
7
Views
951
Electromagnetism: Force on a parabolic wire in uniform magnetic field
    • Calculus and Beyond Homework Help
Replies
20
Views
452

Hot Threads

Recent Insights

Back
Top