Definite Integrals - Average Values, Integration Rules?

Click For Summary
SUMMARY

The discussion focuses on calculating the average value of the function f(t) = (t-3)^2 over the interval [0,6]. The average value is determined using the formula for average value of a continuous function, which involves integrating the function over the specified interval and dividing by the interval's length. The final calculation simplifies to 1/6*(72 - 6*18 + 9*6), confirming the accuracy of the solution provided by the participants.

PREREQUISITES
  • Understanding of definite integrals
  • Familiarity with average value of a function
  • Basic algebra for simplification of expressions
  • Knowledge of integration rules
NEXT STEPS
  • Study the average value theorem for integrals
  • Practice solving definite integrals using various functions
  • Learn about integration techniques such as substitution and integration by parts
  • Explore applications of average values in real-world scenarios
USEFUL FOR

Students studying calculus, mathematics educators, and anyone seeking to understand the application of definite integrals in finding average values of functions.

starless.aeon
Messages
4
Reaction score
0

Homework Statement



Find the average value of the function f(t) = (t-3)^2 on [0,6]

Homework Equations



Average value equation (see below)

The Attempt at a Solution



Okay, I have this:

http://img4.imageshack.us/img4/5338/howthecrap.png

But I don't know how it gets to the last step?
 
Last edited by a moderator:
Physics news on Phys.org
You did great up until the end. Substitute the values of the three integrals into what you have in the line above. You should get 1/6*(72 - 6*18 + 9*6). This answer, when simplified, agrees with mine.
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
2K
Replies
3
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
Replies
5
Views
2K
  • · Replies 13 ·
Replies
13
Views
2K
  • · Replies 18 ·
Replies
18
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
4
Views
1K