# Identities theorem problem

#### sitedesigner

I need help on the following problem. (attached)

Thanks

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#### SteveRives

sitedesigner said:
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

SteveRives said:
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

steven187 said:
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

sitedesigner said:
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 doesnt 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

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#### 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

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.

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