kjp92123
Find the definite integral using the Fundamental Theorem of Calculus.



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kjp92123
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\[\int\limits_{1}^{1} e^x (4e^x) dx\]

92saadz
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see the thing is iruno how to break this ice

92saadz
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is exactly what i need help with

kjp92123
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That's e^(x) by the way
And I know, I'm so lost.

92saadz
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haha yeh this crap makes people lost in formulas man

Im_Hotep55
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so define the fundamental thrm of calculus; then see how that applies :)

kjp92123
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My real question is, I don't know where to start with this problem.

Im_Hotep55
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start by defining the FTC and see how it applies lol.... that is the start

kjp92123
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That does nothing for me.

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

math93
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Yes, what dumbcow said. Then you can take the integral of each part.

Im_Hotep55
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FTC simply says it CAN be done; then you apply the techniques :)

kjp92123
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I don't know how to apply the techniques haha, that's why I'm here!

Im_Hotep55
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the equation editor seems to have distorted the equation ; can you verify it?

kjp92123
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I was given a takehome test, and I'm supposed to teach myself definite integrals and have it due tomorrow.

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

kjp92123
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\[\int\limits_{1}^{1} 1/(e^x) (4e^x) dx\]

math93
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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

Im_Hotep55
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\[\int\limits_{1}^{1} \frac{1}{e^x} (4e^x) dx\]

kjp92123
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^^ that

Im_Hotep55
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frac{top}{bottom} in the editor makes for fancy fractions :)

kjp92123
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Ooo, ok!

Im_Hotep55
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integrate {4/(e^x)  1} dx

Im_Hotep55
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4 (ln(e^x))  x

dumbcow
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do what math93 said

Im_Hotep55
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4xx = 3x
F(x) = 3x right?

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

Im_Hotep55
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close lol

math93
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\[ \frac{4}{e ^{x}}x\] evaluated from 1 to 1

Im_Hotep55
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coulda thunked that 1/u integrates to ln(u)....

Im_Hotep55
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4e^x is just as good i spose :)

math93
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if you sub in your values, you get
(4e^1  1)(4e^1+1)

Im_Hotep55
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i see it..... just blind in my old age

kjp92123
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After the values are substituted in, do I just simplify?

math93
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yes

kjp92123
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So is the final answer (2)?

math93
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Yeah, that's what I got

kjp92123
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So is the answer just (2) by itself? Or is there anything on the opposite side of the equal sign?

math93
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the integral of the original problem = 2, so "2" is the final answer

kjp92123
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Alright, I appreciate the help, I'll use this one as an example to hopefully finish the rest of the problems I have, cheers!

math93
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Good luck!

kjp92123
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Thank you!!