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  1. #1
    Junior Member cinder's Avatar
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    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.
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  2. #2
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    earboth's Avatar
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    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
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  3. #3
    Junior Member cinder's Avatar
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    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?
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  4. #4
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    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
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  5. #5
    Junior Member cinder's Avatar
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    Quote 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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