# simple integration question

• April 9th 2006, 10:11 PM
cinder
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.
• April 9th 2006, 10:34 PM
earboth
Quote:

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
• April 9th 2006, 10:40 PM
cinder
Quote:

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 $2\int_0^3(2x^2-1)dx$?
• April 9th 2006, 10:50 PM
earboth
Quote:

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
• April 9th 2006, 10:52 PM
cinder
Quote:

Originally Posted by earboth
Hello,

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

Greetings

EB

Thanks for the help!