Solving Integral 0 to 3 f(3t)dt Given Question Info

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SUMMARY

The discussion centers on solving the integral from 0 to 3 of f(3t)dt, given the values of two definite integrals: from 0 to 5 of f(x)dx equals 7, and from 1 to 5 of f(x)dx equals 3. The key to solving this problem lies in understanding the relationship between f(3t) and f(x). By substituting u = 3t, the integral can be transformed, allowing for the use of the known integral values to find the solution.

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sapiental
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There was a question on my quiz today that went something like this

the integral 0 to 5 f(x)dx = 7, the integral 1 to 5 f(x)dx = 3

given this information, solve the integral 0 to 3 f(3t)dt.

I had no idea how to do it... How can I compute f(3t)dt given this information? or does the t = x?

Thanks
 
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Think of what kind of function f(3t) is. Try to compare it with the function f(x).
 

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