Thread: Integration

(\int f(x), x, 0, 9) = 4 then (\int f(3x), x, 0 ,3) =

Equals 4/3 but how do you do it using antidifferentiation and not by showing examples?

let



and don't forget the variable of integration is a dummy variable.

try to sub this into the first integral.

so does that mean that 1/3 applies to the first integral. And also the integral is 0, 9 on the first integral and 0,3 on the second..... how does that work out?

Originally Posted by TheEmptySet

let



and don't forget the variable of integration is a dummy variable.

try to sub this into the first integral.

and bring the 3 out from the 3x?

You are given that which, since we can always change a dummy variable, is the same as . To integrate , let u= 3x so x= u/3 as TheEmptySet suggested. Then dx= (1/3)du. When x= 0, u= 0. When x= 3, u= 9. The integral becomes