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Math Help - Definite integral with the integrand being squared?

  1. #1
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    Definite integral with the integrand being squared?

    This is the last question I have for my final review.

    Evaluate: (integrand b=2 a=1 2xdx)^2 - integrand b=2 a=1 (2x)^2 dx

    I think I have the second half - I ended up with 6 after using u sub- but I am having trouble with the first half. Can I foil an integrand?
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  2. #2
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    The way you've written it, the entire integral is squared. Is that what you meant? Or did you mean just the insides, the "2x", to be squared?

    Thank you!
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  3. #3
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    Nope, she has indicated the entire integrand is inside the parenthesis being squared. I was hoping it's as easy as solving and squaring the answer...
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  4. #4
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    The "integrand" is the bit inside the integral; the "integrand" of \int_1^2\, 2x\,dx is "2x". The integral of the square of the integrand would be \int_1^2\, (2x)^2\, dx.

    You have squared the entire integral: \left(\int_1^2\, 2x\, dx\right)^2.

    Which do you mean?

    If the former, then integrate 4x^2 from 1 to 2. If the latter, integrate 2x from 1 to 2, and then square the numerical result.
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  5. #5
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    Sorry, I meant integral. Yes, the entire integral is being squared as you have in the former. Thanks for verifying how to solve!
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