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If the integral from 0 to 8 of f(x)=4, then calculate the integral of f(4x) from 0 to 2.

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suppose ∫ f(x) dx = F(x)

Then

∫[0,8] f(x) dx = F(8)-F(0) = 4

∫[0,2] f(4x) dx
= ∫[0,2] 1/4 f(4x) d(4x)
= 1/4(F(8)-F(0)) = 1

check:

∫[0,8] x^2 dx = 512/3
∫[0,2] (4x)^2 dx = 16(8/3) = 128/3

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