If-1-4-f-x-dx-5-what-is-the-value-of-0-1-f-3x-1-dx-

Question Number 22166 by Joel577 last updated on 12/Oct/17

If \underset{1}{\int^{4}} f (x) d x = 5

what is the value of \underset{0}{\int^{1}} f (3 x + 1) d x ?

Answered by ajfour last updated on 12/Oct/17

I = \int_{0}^{1} f (3 x + 1) d x

l e t 3 x + 1 = t \Rightarrow d x = \frac{d t}{3}

c l e a r l y t h e n x = 0 \Rightarrow t = 1

a n d w h e n x = 1, t = 4

s o I = \frac{1}{3} \int_{1}^{4} f (t) d t = \frac{1}{3} \int_{1}^{4} f (ρ) d ρ

= \frac{1}{3} \int_{1}^{4} f (x) d x = \frac{1}{3} \times 5 = \frac{5}{3} .

Commented by Joel577 last updated on 13/Oct/17

t h a n k y o u v e r y m u c h

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