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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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?

Mathematics
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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 ?
Yes, sorry, I didn't think I could add equations when I was writing up the question.
no problem :) just to clarify are those negative signs outside integrals, also present in the question ?

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Other answers:

Yes there are, would that make a difference to the answer of my question?
yes thats because now \(\int \limits_{-4}^{1}f(x) = -4\)
Oh I see, why's that?
multiplying -1 on both sides
Oh... RIGHT! Can't believe I missed that!! Thanks for your help :)
welcome ^_^ so whats your new final answer?
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
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!
welcome ^_^

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