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?

Question

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?

hartnn · Answer

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

clarence · Answer

Yes, sorry, I didn't think I could add equations when I was writing up the question.

hartnn · Answer

no problem :)

just to clarify

are those negative signs outside integrals, also present in the question ?

clarence · Answer

Yes there are, would that make a difference to the answer of my question?

hartnn · Answer

yes

thats because now 

$\int \limits_{-4}^{1}f(x) = -4$

clarence · Answer

Oh I see, why's that?

hartnn · Answer

multiplying -1 on both sides

clarence · Answer

Oh... RIGHT! Can't believe I missed that!! Thanks for your help :)

hartnn · Answer

welcome ^_^

so whats your new final answer?

hartnn · 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

clarence · Answer

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!

hartnn · Answer

welcome ^_^