Successive Integrals: Examining 1st Integral y_1(t)

  • Context: Undergrad 
  • Thread starter Thread starter SuperCat
  • Start date Start date
  • Tags Tags
    Integrals
Click For Summary
SUMMARY

The discussion centers on the clarification of the first integral y_1(t) in the context of successive integrals. Participants confirm that the first integral should indeed be expressed as ∫_{-∞}^t y(τ) dτ, indicating a typo in the textbook. The distinction between using 't' for the first integral and 'τ' for the second integral is highlighted, emphasizing the importance of consistency in notation for clarity in mathematical expressions.

PREREQUISITES
  • Understanding of integral calculus
  • Familiarity with notation in mathematical integrals
  • Knowledge of successive integrals
  • Basic concepts of limits in calculus
NEXT STEPS
  • Review the properties of successive integrals in calculus
  • Study the implications of variable substitution in integrals
  • Explore common typographical errors in mathematical texts
  • Learn about the notation conventions in integral calculus
USEFUL FOR

Students of calculus, educators teaching integral calculus, and anyone involved in mathematical analysis or textbook editing will benefit from this discussion.

SuperCat
Messages
26
Reaction score
1
My textbook shows the following example of successive integrals:

Does the 1st integral y_1(t) have a typo? Shouldn't the integral be taken with regards to Tau?
If not, I would appreciate an explanation of why the 1st successive integral is taken with regards to t, but in the second it is taken with regards to Tau.
 
Last edited:
Physics news on Phys.org
SuperCat said:
My textbook shows the following example of successive integrals:

bea3edbefa003bb45e863894e4a9b56f.png


Does the 1st integral y_1(t) have a typo? Shouldn't the integral be taken with regards to Tau?
If not, I would appreciate an explanation of why the 1st successive integral is taken with regards to t, but in the second it is taken with regards to Tau.
I believe you're right about this being a typo.
The integral should be ##\int_{-\infty}^t y(\tau) d\tau##.
 
  • Like
Likes   Reactions: SuperCat
Mark thank you for your reply. I had a feeling that it didn't make sense, but I always feel a lot more comfortable getting a second opinion. This is now resolved.
 

Similar threads

Undergrad Integration with different infinitesimal intervals
  • · Replies 31 ·
2
Replies
31
Views
4K
Undergrad On convolution theorem of Laplace transform: Schiff
  • · Replies 4 ·
Replies
4
Views
2K
High School How do physicists know if limits exist, things are integrable, etc?
  • · Replies 12 ·
Replies
12
Views
3K
Undergrad Integration Limits Changing in Double Integral Order Change
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Should the function f to be continuous for applying MVTI or not?
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad Equivalence of alternative definitions of conservative vector fields and line integrals in different metric spaces
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Is My Calculus of Variations Approach Correct?
  • · Replies 12 ·
Replies
12
Views
3K
Undergrad Did Math DF's integral calculator make a glaring mistake?
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Testing for Divergence using the Integral Test
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Numerical Integration twice (acceleration to displacement)
  • · Replies 5 ·
Replies
5
Views
5K