Question

Let the following be true.
b
(integral of)f(x) dx=7
a

Find the value of the following integral.

b+4
(integral of) f(x−4) dx=
a+4

Answer 1

the a+4 and the b+4 tell you that the endpoints are both being shifted over 4 units to the right

going from f(x) to f(x-4) shifts the entire function curve 4 units to the right

Answer 2

so essentially, everything (endpoints + function) has moved 4 units to the right

the area stays the same

Answer 3

so it would still be 7?

Answer 4

yes

Answer 5

wow that makes so much sense! thank you!!

Answer 6

all of these translations preserve shape, area, distance, etc

Answer 7

i make my life harder haha

Answer 8

thanks again!

Answer 9

you're welcome