Question

Medal and fan!
Given that the area of B=5, integral of (-2,1) f(x)dx= 2, and integral of (1,8) f(x) dx = -4.
1) integral of (-2,6) f(x) dx
2) Integral of (1,6) f(x) dx
3) integral of (6,8) f(x) dx
4) integral of (-2,8) [absolute value of f(x)] dx
5) integral of (-2,8) f(x) dx

Answer 1

I don't understand the problem. Is it
\(\Large \int_{-2}^{1} f(x)dx =2\\ \Large \int_{1}^{8} f(x)dx =-4\)
and then???

Answer 2

yes, then solve the 5 exercises with the same information above. I think it has to do with integrating even/odd functions? because I am correcting

Answer 3

oh, I got it

Answer 4

that is the given information and you have to answer 5 questions bellow, right? with the whole Area is 5, right?

Answer 5

Yes, I think so

Answer 6

It's not hard. I do the first one for you. You can imitate for the leftover, deal?

Answer 7

ok

Answer 8

first off, the whole area is 5 it means after finding the total area is 5-->\[ \int_{-2}^{1} f(x) dx +\int_{1}^{6} f(x)dx=\int_{-2}^{6}f(x)dx =5\]

Answer 9

but it doesn't help much, I do the next one for you as sample
From part 1) you have
\[\int_{-2}^{1} f(x) dx +\int_{1}^{6} f(x)dx=\int_{-2}^{6}f(x)dx =5\\\]
\[\rightarrow\int_{1}^{6} f(x)dx=\int_{-2}^{6}f(x)dx -\int_{-2}^{1} f(x) dx = 5-2 =3 \]

Answer 10

can you do the rest?

Answer 11

I did #5 and only got to \[\int\limits_{-2}^{8} f(x) dx = \int\limits_{2}^{1} f(x) dx + \int\limits_{1}^{8} f(x) dx\]
The only thing is that I don't know how you get the 5 from the first and the 3 from the second exercise?

Answer 12

the given information is " Given the area of B is 5"

Answer 13

I get where you got the 5-2 from the info, but then for the 5th exercise I did it would be ? - (-4)?

Answer 14

wait, I' ll scan the explanation for you

Answer 15

Ok yes, the other one I'm having total difficulty is the one with the absolute value exercise, a little hint for that one? :)

Answer 16

just take positive value, it means 4 instead of -4

Answer 17

and for \[\int\limits_{6}^{8} f(x)dx = \int\limits_{?}^{?} f(x) dx - \int\limits_{1}^{8} f(x)dx = ? -( -4) ?\]

Answer 18

you have 1to 6 and 1to 8 subtract them to get 6 to8

Answer 19

Alright thanks a lot! Great explanations.