# Given an integral, find the others

• Jan 13th 2013, 06:51 PM
Chaim
Given an integral, find the others
Given 05f(x)dx=10 and 57f(x)dx=3, (by the way, that means the intervals for the first one are 0 and 5, and the 2nd one is 5 and 7)
Find...
(a)07f(x)dx and (b)05f(x)dx

I wasn't sure how to do this, because there were no variables, so I thought f(x)dx=3, but then the intervals are different.
So for like the first one, I know that the intervals are [0, 7]
Then what we're integrating is f(x)dx

But I'm a bit confused on how to start off with that.
I'm used to integrating when given an equation, but this one is giving the function.

Can someone explain to me?
Thanks.
• Jan 13th 2013, 06:55 PM
Deveno
Re: Given an integral, find the others
you're supposed to use THIS theorem: for a < b < c,

$\displaystyle \int_a^b f(x)\ dx + \int_b^c f(x)\ dx \ = \int_a^c f(x)\ dx$
• Jan 13th 2013, 07:34 PM
Chaim
Re: Given an integral, find the others
Quote:

Originally Posted by Deveno
you're supposed to use THIS theorem: for a < b < c,

$\displaystyle \int_a^b f(x)\ dx + \int_b^c f(x)\ dx \ = \int_a^c f(x)\ dx$

Oh!
I see, thanks!
So I'm a bit confused, but making sure, that's the Additive Interval Property right?

And just wondering, do I just give the 2 intervals that were given, to find the solutions to (a) and (b)?
Like what would be the variable for a, b, c, and d.

Would it be like this?
05f(x)dx+57f(x)dx

That would become what (a) is like.
But after that, what would you do, if that was right?
By the way, the answer is 13 in the book.
• Jan 13th 2013, 08:24 PM
Prove It
Re: Given an integral, find the others
Surely you can see that when you apply the additive property that 10 + 3 = 13...
• Jan 13th 2013, 09:04 PM
Deveno
Re: Given an integral, find the others
ok, look, definite integrals and indefinite integrals are VERY different.

indefinite integrals: plug in a function, get another function (plus a constant):

$\displaystyle \int f(x)\ dx = F(x) + C$

definite integrals: plug in a function, get a NUMBER:

$\displaystyle \int_a^b f(x)\ dx = F(b) - F(a)$

you're already given "the numbers", you don't NEED the function F (or f).