Given 2 Integrals, How to solve other Integrals?

[jeckel7234]

given
∫(2-5) f(x)dx=5 and ∫(4-5) f(x)dx=∏ , find


a)
∫(5-5) f(x)dx =

b)
∫(5-4) f(x)dx =

c)
∫(2-4 f(x)dx =


Im going over old tests of mine to get ready for my final, and I can't find anywhere in my notes how I solved this, I originally got (a. 0 b. ∏ c. 5-∏). Can someone just explain the process of how to solve this. I understand b) by changing the sign and swapping the limits equals one of the given integrals, I just can't understand how I got A and C?

Thanks and Hi everyone

 

[Mute]

given
∫(2-5) f(x)dx=5 and ∫(4-5) f(x)dx=∏ , finda)
∫(5-5) f(x)dx =

b)
∫(5-4) f(x)dx =

c)
∫(2-4 f(x)dx =Im going over old tests of mine to get ready for my final, and I can't find anywhere in my notes how I solved this, I originally got (a. 0 b. ∏ c. 5-∏). Can someone just explain the process of how to solve this. I understand b) by changing the sign and swapping the limits equals one of the given integrals, I just can't understand how I got A and C?

Thanks and Hi everyone

Well, I think (a) should be rather obvious... Take another look. =P

As for (c), it is just a linear combination of the first two integrals you were given. See if you can figure out in what way you can add/subtract the integrals to get (c).

Also, are there given limits of integration? You haven't listed them here, and without them it's not obvious that you need to swap them to get the result for (b) - without the limits of integration the answer could just as well be $-\pi$.

 

[jeckel7234]

Well, I think (a) should be rather obvious... Take another look. =P

As for (c), it is just a linear combination of the first two integrals you were given. See if you can figure out in what way you can add/subtract the integrals to get (c).

Also, are there given limits of integration? You haven't listed them here, and without them it's not obvious that you need to swap them to get the result for (b) - without the limits of integration the answer could just as well be $-\pi$.

lol yep a was that easy, its kinda of sad I needed someone to say look again and don't be in idiot about it. Thanks for that

b) That was a typo on my behalf, I had -∏ down

c) ∫(2-5) - ∫(4-5)