Question

Find the definite integral using the Fundamental Theorem of Calculus.

Answer 1

\[\int\limits_{-1}^{1} e^-x (4-e^x) dx\]

Answer 2

see the thing is iruno how to break this ice

Answer 3

is exactly what i need help with

Answer 4

That's e^(-x) by the way
And I know, I'm so lost.

Answer 5

haha yeh this crap makes people lost in formulas man

Answer 6

so define the fundamental thrm of calculus; then see how that applies :)

Answer 7

My real question is, I don't know where to start with this problem.

Answer 8

start by defining the FTC and see how it applies lol.... that is the start

Answer 9

That does nothing for me.

Answer 10

expand it and you will get 4e^-x - 1

Answer 11

Yes, what dumbcow said. Then you can take the integral of each part.

Answer 12

FTC simply says it CAN be done; then you apply the techniques :)

Answer 13

I don't know how to apply the techniques haha, that's why I'm here!

Answer 14

the equation editor seems to have distorted the equation ; can you verify it?

Answer 15

I was given a take-home test, and I'm supposed to teach myself definite integrals and have it due tomorrow.

Answer 16

FTC says the definite integral = F(1) - F(-1)
but you have to find F(x) by taking anti-derivative of f(x)

Answer 17

\[\int\limits_{-1}^{1} 1/(e^x) (4-e^x) dx\]

Answer 18

If you integrate 4e^-x, you would get -4e^-x.
Then, integrate 1 and you get x
So then you have -4e^-x - x evaluated from -1 to 1

Answer 19

\[\int\limits_{-1}^{1} \frac{1}{e^x} (4-e^x) dx\]

Answer 20

^^ that

Answer 21

frac{top}{bottom} in the editor makes for fancy fractions :)

Answer 22

Ooo, ok!

Answer 23

integrate {4/(e^x) - 1} dx

Answer 24

4 (ln(e^x)) - x

Answer 25

do what math93 said

Answer 26

4x-x = 3x

F(x) = 3x right?

Answer 27

no F(x) =-4e^-x - x

Answer 28

close lol

Answer 29

\[ \frac{-4}{e ^{x}}-x\] evaluated from -1 to 1

Answer 30

coulda thunked that 1/u integrates to ln(u)....

Answer 31

4e^-x is just as good i spose :)

Answer 32

if you sub in your values, you get
(-4e^-1 - 1)-(-4e^-1+1)

Answer 33

i see it..... just blind in my old age

Answer 34

After the values are substituted in, do I just simplify?

Answer 35

yes

Answer 36

So is the final answer (-2)?

Answer 37

Yeah, that's what I got

Answer 38

So is the answer just (-2) by itself? Or is there anything on the opposite side of the equal sign?

Answer 39

the integral of the original problem = -2, so "-2" is the final answer

Answer 40

Alright, I appreciate the help, I'll use this one as an example to hopefully finish the rest of the problems I have, cheers!

Answer 41

Good luck!

Answer 42

Thank you!!