Any help will be appreciated assuming a pretty easy integral

[IntegrateMe]

Any help will be appreciated...assuming a pretty easy integral...

∫f(t) dt = 9 [0, 1]

Find:

∫f(10t)dt [0, 0.1]
∫f(1 - 10t)dt [0, 0.1]

Any idea on how to get started with this one?

 

[Dick]

∫f(t) dt = 9 [0, 1]

Find:

∫f(10t)dt [0, 0.1]
∫f(1 - 10t)dt [0, 0.1]

Any idea on how to get started with this one?

Change variables with a u-substitution. For the first one try u=10t. What is du?

 

[IntegrateMe]

10dt!

 

[Dick]

10dt!

Ok, so change the t integral to a u integral.

 

[IntegrateMe]

1/10∫f(u)du ?

 

[Dick]

1/10∫f(u)du ?

Looks good so far. And what are the u limits? The t limits were [0,0.1].

 

[IntegrateMe]

From 0 to 0.1.

Does ∫f(u)du = 9?

 

[Dick]

From 0 to 0.1.

Does ∫f(u)du = 9?

It won't be 9, if the u limits are 0 to 0.1. But they aren't. If t=0.1, what's the corresponding u?