## anonymous 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?

1. hartnn

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

2. anonymous

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

3. hartnn

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

4. anonymous

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

5. hartnn

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

6. anonymous

Oh I see, why's that?

7. hartnn

multiplying -1 on both sides

8. anonymous

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

9. hartnn

10. hartnn

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. anonymous

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

welcome ^_^

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