Question

Integral question see attached images

Answer 1

I'm not really sure how to do this I did the anti-derivative for both of fx then used the 1st fund thrm of calc

Answer 2

just break it into two integrals
what are the bounds? where is the breaking point in the function?

Answer 3

hmm and just do f(b)-f(a) for both? and add them together?

Answer 4

what do f(a) oand f(b) represent to you?
I don't see how that way of writing things helps us...

Answer 5

F(b)-F(a) b being the top value and a being the bottom value listed on the integral

Answer 6

b=7 and a=-1

Answer 7

but the definition of f(x) is not the same throughout

Answer 8

not f(x) F as in the anti-derivative lol

Answer 9

I understand what you are saying, but hear me...

Answer 10

Yeah so how do I deal with that lol?

Answer 11

we have to treat this like two different integrands f(x) to begin with
have you heard the word "integrand" before?

Answer 12

no I haven't were in calc I

Answer 13

rather I am in calc 1

Answer 14

it's the function under the integral sign
i.e. the function we area integrating is called the "integrand"

Answer 15

we are*

Answer 16

ahhh

Answer 17

so at what value of x does the definition of the integrand f(x) change ?

Answer 18

1

Answer 19

correct?

Answer 20

yes, very good!
so we have two integrals, with two different integrands....

Answer 21

from x=-1 to x=1 the integrand is what?

Answer 22

x^2/2?

Answer 23

rather x because the integrand is what we are doing to integrate right?

Answer 24

in\[\int f(x)dx\]the integrand is just f(x)
i.e. in \\[\int x^2dx\] the integrand is the function \(f(x)=x^2\)

Answer 25

how did you get x^2?

Answer 26

ohhhhh

Answer 27

example only

Answer 28

wow sorry half asleep

Answer 29

lol

Answer 30

yeah so its x!

Answer 31

for -1 to 1

Answer 32

yes

Answer 33

so we have that now what? Integrate get x^2/2 then what?

Answer 34

do -1^2/2 - 1^2/2?

Answer 35

which is 0 lol

Answer 36

you are right that the answer is zero, but it should be
1^2/2 - 1^2/2
the way you wrote it would result in -1

Answer 37

so the first integral is zero...
what is the second integral?

Answer 38

1 to 7 the integral being ln |x|?

Answer 39

muahahahaha! thats right! thanks!!!!!

Answer 40

you are welcome :)

Answer 41

thank you for being a good student

Answer 42

^.^