Any help will be appreciated assuming a pretty easy integral

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Homework Help Overview

The discussion revolves around evaluating integrals involving a function f(t) given that the integral of f(t) from 0 to 1 equals 9. Participants are tasked with finding the integrals of f(10t) and f(1 - 10t) over the interval from 0 to 0.1.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss using u-substitution to change the variable in the integrals. There is a focus on determining the correct limits of integration after substitution and questioning the value of the integral based on those limits.

Discussion Status

The discussion is active with participants exploring the implications of variable substitution and the corresponding limits. Some guidance has been offered regarding the substitution process, but there is no explicit consensus on the values of the integrals or the limits after substitution.

Contextual Notes

Participants are working under the assumption that the integral of f(t) from 0 to 1 equals 9, but there is uncertainty regarding how this value translates to the new limits after substitution.

IntegrateMe
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Any help will be appreciated...assuming a pretty easy integral...

∫f(t) dt = 9 [0, 1]

Find:

∫f(10t)dt [0, 0.1]
∫f(1 - 10t)dt [0, 0.1]

Any idea on how to get started with this one?
 
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IntegrateMe said:
∫f(t) dt = 9 [0, 1]

Find:

∫f(10t)dt [0, 0.1]
∫f(1 - 10t)dt [0, 0.1]

Any idea on how to get started with this one?

Change variables with a u-substitution. For the first one try u=10t. What is du?
 


10dt!
 


IntegrateMe said:
10dt!

Ok, so change the t integral to a u integral.
 


1/10∫f(u)du ?
 


IntegrateMe said:
1/10∫f(u)du ?

Looks good so far. And what are the u limits? The t limits were [0,0.1].
 


From 0 to 0.1.

Does ∫f(u)du = 9?
 


IntegrateMe said:
From 0 to 0.1.

Does ∫f(u)du = 9?

It won't be 9, if the u limits are 0 to 0.1. But they aren't. If t=0.1, what's the corresponding u?
 

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