Conceptual integral shift/translation.

In summary, the question is asking for the integral of g(2-u)du on the interval [0,2] given that the integral of g(u)du on the interval [0.2] is 12. The attempt at a solution involves substituting v=2-u and rewriting the limits and du, but it is unclear what the final result is.
  • #1
CandyApples
28
0

Homework Statement


Given that the integral of g(u)du on the interval [0.2] is 12, what is g(2-u)du on the interval [0,2]


Homework Equations


f on [a,b] is F(b) - F(a).


The Attempt at a Solution


Switching from positive to negative t flips the limits to [2,0]. This would yield -12 instead of 12. F(2) on 0,2 would just be 4. The answer of -8, however is not correct. Have I violated order of operations or am I missing a concept?
 
Physics news on Phys.org
  • #2
Welcome to PF!

Hi CandyApples! Welcome to PF! :smile:

(have an integral: ∫ :wink:)
CandyApples said:

Homework Statement


Given that the integral of g(u)du on the interval [0.2] is 12, what is g(2-u)du on the interval [0,2]

I'm not sure what you've done. :confused:

Put v = 2 - u, and rewrite du and the limits …

what do you get? :smile:
 

FAQ: Conceptual integral shift/translation.

What is a conceptual integral shift/translation?

A conceptual integral shift/translation refers to the process of changing the variables in an integral equation to better understand and solve a problem. It involves shifting the origin and changing the scale of the integral, resulting in a new integral with different limits and variables.

Why is it important to use conceptual integral shift/translation?

Conceptual integral shift/translation allows for a deeper understanding of integral equations and can make them easier to solve. It also helps to visualize and interpret the results of the integral in a more meaningful way.

How does conceptual integral shift/translation differ from traditional integration methods?

Traditional integration methods involve using techniques such as substitution, integration by parts, and partial fractions to solve integrals. Conceptual integral shift/translation, on the other hand, involves changing the variables in the integral equation to simplify the problem.

Can conceptual integral shift/translation be applied to all types of integrals?

Yes, conceptual integral shift/translation can be applied to all types of integrals, including definite and indefinite integrals, as long as the integral has a variable that can be shifted or translated.

Are there any limitations to using conceptual integral shift/translation?

While conceptual integral shift/translation can be a useful tool in solving integrals, it may not always be necessary or applicable, especially for simpler integrals that can be solved using traditional methods. It is important to understand the purpose and limitations of this method before applying it to a problem.

Similar threads

A few questions to make sure I understand Fourier series
Replies
3
Views
1K
Interval of convergence for Taylor series exp of 1/x^2
Replies
10
Views
4K
Find v(t) from Newton's Second Law and Differential Equation
Replies
3
Views
2K
Calculating the Fourier integral representation of f(x)
Replies
9
Views
3K
I Substitution in a definite integral
Replies
6
Views
2K
The integral of a function ##f(x)## from its graph
Replies
15
Views
2K
Missing some fundamental understanding- U-sub w/ radicals
Replies
8
Views
1K
Time-shifted Integral with Unit Impulse Function
Replies
4
Views
2K
Integrating with Changing Intervals: Finding the Area Between Two Curves
Replies
2
Views
1K
Determine the truth of the following statements
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top