simple integration question

**cinder** · April 9th 2006, 09:11 PM

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.

**earboth** · April 9th 2006, 09:34 PM

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

**cinder** · April 9th 2006, 09:40 PM

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 $2\int_0^3(2x^2-1)dx$ ?

**earboth** · April 9th 2006, 09:50 PM

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

**cinder** · April 9th 2006, 09:52 PM

Originally Posted by earboth

Hello,

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

Greetings

EB

Thanks for the help!

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