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Clarence

  • one year ago

For this question: Suppose −∫1(top)−4(bottom) for f(x)dx = 4 and −∫1(top)−4(bottom) g(x)dx=−4. What is the value of −∫1(top)−4(bottom)(3f(x)−4g(x))dx. Wouldn't it just be 3(4)-4(-4) and hence would equal 28?

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  1. hartnn
    • one year ago
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    \(\large -\int \limits_{-4}^{1}f(x)dx = 4 \\ \Large -\int \limits_{-4}^{1}g(x)dx = -4 \\ \Large -\int \limits_{-4}^{1}3f(x) -4g(x) = .. ?\) this is your question ?

  2. clarence
    • one year ago
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    Yes, sorry, I didn't think I could add equations when I was writing up the question.

  3. hartnn
    • one year ago
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    no problem :) just to clarify are those negative signs outside integrals, also present in the question ?

  4. clarence
    • one year ago
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    Yes there are, would that make a difference to the answer of my question?

  5. hartnn
    • one year ago
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    yes thats because now \(\int \limits_{-4}^{1}f(x) = -4\)

  6. clarence
    • one year ago
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    Oh I see, why's that?

  7. hartnn
    • one year ago
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    multiplying -1 on both sides

  8. clarence
    • one year ago
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    Oh... RIGHT! Can't believe I missed that!! Thanks for your help :)

  9. hartnn
    • one year ago
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    welcome ^_^ so whats your new final answer?

  10. hartnn
    • one year ago
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    actually it wouldn't make a difference in the final answer because there is a negative sign outside the 3rd integral too! 3(4) - 4(-4) =28 -3 (-4) +4(4) = 28 :D

  11. clarence
    • one year ago
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    Aha, yeah, I reached a mental blank whilst trying to figure that out and trying to make sense of it all in my head :P Thanks for the clarification!

  12. hartnn
    • one year ago
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    welcome ^_^

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