Understanding the Identities Theorem: Can You Solve this Problem?

[sitedesigner]

I need help on the following problem. (attached)

Thanks

 

[SteveRives]

I need help on the following problem. (attached)

Thanks

Draw a picture of some curve (i.e. make a guess about what the curve looks like), shade the regions given, then think about what they are asking -- perhaps the answer will become obvious...

 

[steven187]

hello there

well
f '(5)-f '(2) =11
f '(11)-f '(8) =27
f '(5)-f '(8)+f '(11)-f '(2)=f '(5)-f '(2)+f '(11)-f '(8) =11+27=38
I hope you do know what i have done, take care

steven

 

[sitedesigner]

Draw a picture of some curve (i.e. make a guess about what the curve looks like), shade the regions given, then think about what they are asking -- perhaps the answer will become obvious...

I'm not sure if 38 is the correct answer though

 

[sitedesigner]

hello there
f '(5)-f '(8)+f '(11)-f '(2)=f '(5)-f '(2)+f '(11)-f '(8) =11+27=38
steven

can you explain how you got to that part?

 

[steven187]

hello there

I'm not sure if 38 is the correct answer though

why arnt you sure, what are you having doubts about? explain your thoughts?

steven

 

[sitedesigner]

even though i scanned it in there, it was a mere guess.

 

[steven187]

hello there

well I have basically given you the answer all you have to do now is interpret it, you must have some prior knowledge of knowing the basics of how to understand this question, by the way they were suppose to be capital F's

F(5)-F(2) =11
F(11)-F(8) =27
F(5)-F(8)+F(11)-F(2)=F(5)-F(2)+F(11)-F(8) =11+27=38

steven

 

[sitedesigner]

can you state the theorem or definition that makes that true? I understand the format it's in, but not why it works. Even visualizing it doesn't make sense :(

 

[sitedesigner]

actually, i drew myself a picture, and now i understand it now :)

 

[sitedesigner]

guess a picture is worth a thousand words... here it is attached

 

[sitedesigner]

i really appreciate the quick response... that's what makes physicsforums a great place!

 

[steven187]

you welcome

well we are happy for you to be part of this forum, by the way you havnt told us what your answer was?

 

[sitedesigner]

When i was doing that problem, I had originally put the answer as 38 because somewhere in the back of my mind i had recalled reading about adding and subtracting integrals.

I didnt understand what the answer was, but after i drew the picture, it became more clear :) The answer is 38.

 

[Yegor]

can you state the theorem or definition that makes that true? I understand the format it's in, but not why it works.

$$\int_a^b f(x) dx =\int_a^c f(x) dx +\int_c^b f(x) dx$$
$$\int_a^b f(x) dx =-\int_b^a f(x) dx$$
Do you know these identities?
These 2 make given problem almost formal.