1. simple integration question

How do you know when you can move something outside the integral to be later multiplied by the integrated function?

For example,

$\int_0^4\pi(x^2)dx$ vs. $\pi\int_0^4(x^2)dx$

And please remember, this is Calculus I. Thanks.

2. Originally Posted by cinder
How do you know when you can move something outside the integral to be later multiplied by the integrated function?

For example,

$\int_0^4\pi(x^2)dx$ vs. $\pi\int_0^4(x^2)dx$

And please remember, this is Calculus I. Thanks.
Hello,

if you've got a constant factor (-3 or 2 or $\pi$ or e or ...) then you can put it outside the integral.

With sums you can sometimes split the integral into two or more (maybe simpler) integrals.

Greetings

EB

3. Originally Posted by earboth
Hello,

if you've got a constant factor (-3 or 2 or $\pi$ or e or ...) then you can put it outside the integral.

With sums you can sometimes split the integral into two or more (maybe simpler) integrals.

Greetings

EB
If you have $\int_0^3(4x^2-2)dx$, can you make it $\int_0^32(2x^2-1)dx$ giving $2\int_0^3(2x^2-1)dx$?

4. Originally Posted by cinder
If you have $\int_0^3(4x^2-2)dx$, can you make it $\int_0^32(2x^2-1)dx$ giving $2\int_0^3(2x^2-1)dx$?
Hello,

you've got it. Exactly what you should (or can) do.

Greetings

EB

5. Originally Posted by earboth
Hello,

you've got it. Exactly what you should (or can) do.

Greetings

EB
Thanks for the help!