How do I use substitution to solve these integrals?

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SUMMARY

The discussion focuses on solving integrals using substitution, specifically for the function ∫f(t)dt=11 over the interval [0,1]. The first integral, ∫f(4t)dt from 0 to 0.25, is correctly evaluated as (1/4) * ∫f(u)du from 0 to 1, resulting in 11/4. The second integral, ∫f(1−4t)dt from 0 to 0.25, requires a similar substitution approach, while the third integral, ∫f(3−8t)dt from 0.25 to 0.375, also follows the substitution method but needs clarification on the appropriate substitution to use.

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Please help me calculate these integrals.
Suppose that ∫f(t)dt=11 [0,1]. Calculate each of the following.
A. ∫f(4t)dt [0,0.25] =

B. ∫f(1−4t)dt [0,0.25] =

C. ∫f(3−8t)dt [0.25,0.375] =

I did the first one and I believe is right and I try to do the 2nd and 3rd one similarily and can't get them .:rolleyes:
u=4t
du=4dt, or
dt=(1/4)du
∫f(4t)dt [0,0.25]
=∫f(u)(1/4)du [0,4*0.25]
=(1/4)∫f(u)du [0,1]
=(1/4)*11
=11/4
 
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The second one is almost exactly the same. What substitution would you try??
 

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