Evaluating definite integrals by subsitution

[nuclearpenguin]

I'm having trouble figuring out how to do this problem. I can't find anything in my book that talks about it, but it's one of the exercise problems.
Can anyone help me?

FIND ∫ b=1, a=0 f(3x +1)dx if ∫b=4, a=1 f(x)dx=5

 

[Deleted member 4993]

I'm having trouble figuring out how to do this problem. I can't find anything in my book that talks about it, but it's one of the exercise problems.
Can anyone help me?

FIND ∫ b=1, a=0 f(3x +1)dx if ∫b=4, a=1 f(x)dx=5

substitute

u = 3x + 1

du = 3* dx

at x=1 → u = 4 and at x= 0 → u = 1

Now you are given \(\displaystyle \displaystyle{\int_1^4f(x) dx \ = \ 5}\)

and you need to calculate:

\(\displaystyle \displaystyle{\int_1^4f(u) du \ = \ ?}\)