If-f-x-continue-in-1-30-and-6-30-f-x-dx-30-then-1-9-f-3y-3-dy-

Question Number 109546 by bemath last updated on 24/Aug/20

I f f (x) c o n t i n u e i n [1, 30] a n d

\underset{6}{\int^{30}} f (x) d x = 30, t h e n \underset{1}{\int^{9}} f (3 y + 3) d y =__

Commented by kaivan.ahmadi last updated on 24/Aug/20

t = 3 y + 3 \Rightarrow d t = 3 d y \Rightarrow d y = \frac{1}{3} d t

y = 1 \Rightarrow t = 6

y = 9 \Rightarrow t = 30

\frac{1}{3} \int_{6}^{30} f (t) d t = \frac{1}{3} \times 30 = 10

Commented by bemath last updated on 24/Aug/20

c o o l l . . t h a n k s

Answered by 1549442205PVT last updated on 24/Aug/20

Put x = 3 y + 3 \Rightarrow dx = 3 dy . Then

\int_{1}^{9} f (3 y + 3) dy = \frac{1}{3} \int_{6}^{30} f (x) dx = \frac{1}{3} \times 30 = 10