If-1-4-f-x-dx-6-then-1-4-f-5-x-dx-

Question Number 127616 by bramlexs22 last updated on 31/Dec/20

If \int_{1}^{4} f (x) dx = 6, then \int_{1}^{4} f (5 - x) dx ?

Commented by liberty last updated on 31/Dec/20

let 5 - x = X \Rightarrow dx = - dX

if x = 4 \Rightarrow X = 1 \land if x = 1 \Rightarrow X = 4

then \int_{1}^{4} f (5 - x) dx = \int_{4}^{1} f (X) (- dX)

= \int_{1}^{4} f (X) dX = 6 .

hahaha

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