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anonymous
 5 years ago
e^.07(10t)[10,1) find the definite integral
anonymous
 5 years ago
e^.07(10t)[10,1) find the definite integral

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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0[10,1) is a little backwards... (1,10] is that e^.07 times (10t)? or is the last part included in the exponent?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{1}^{10} e^.07(10t)\]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0so it aint included as the exponent..makes it alittle easier :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0e^.07 is a constant, so pull it out of the way

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0(S) (10t) dt > 10t  (1/2)t^2 F(t) = [10t  (t^2)/2] e^.07

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0F(10)  F(1) will be the answer

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0(100  50)e^.07  (10.5)e^.07 (50  9.5) e^.07 (40.5) e^.07 if I did it right in me head :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0that might be alittle off, did you mean to exclude 1 as an option?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no 1 is included. now I'm understanding

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0whew!!.... cause in the top {10,1) means everything from 10 to 1 but not including 1 :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no i just want it for 10 and 1

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0then were good with it :) I got some idea for how to find it if it approaches 1, but nothing ti be sure about :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ive got another one its its kinda hard what you think

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0I can take a stab at it..... im ok with failure :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0is it one thats already posted? or you need to write it up?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0im going to write it now

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{15}\]e^0.05e^.06(15t)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0to clean it up... is that: e (e) (15t) ??

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0or is that: e^e^(15t)?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0i assume the first one :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0recall that like bases when multiplies add exponents, for example: 5^3 5^5 = 5^(3+5) = 5^8 so, e^.06 e^.06 = e^.11 which is still a constant and can be pulled out...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0you can see the typo right....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0that leaves us with: (S) 15t dt > 15t  (t^2)/2  [15,0] F(t) = [15t  (t^2)/2] e^.11 since F(0) = 0 the only important on is F(15) F(15) = [15(15)  15(15)/2] e^.11 = [225  112.5] e^.11 F(15)= 112.5 e^.11

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{15}e^.05e.06(15t)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0this is how it looks exactly will u get the same answer or does this makes a difference

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0is that .06 an exponent?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0(e^.05) (e^.06) (15t) is what I integrated :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0that equation option down there is useful for some things, but I can never get it to do what I want....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{15} e^{.05} e^{.06} \left( 15t \right)\]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0\[= (112.5) e ^{.11}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it its e^0.5.e^.06 the 15t is beside the .06 in exponential form

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok so what will happen to the ^(15t)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{15} e ^{.05} e^{.06\left( 15t \right)}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes that's exactly what it is

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0ok....we can pull out that first e, its nothing but a constant

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0go ahead and distribute the .06 thru the (...)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0If we can get this into the form: (S) Du e^u , then it suits up to e^u....does that make sense?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0think back to derivatives... e^2x goes down to 2 e^2x right? does that ring a bell?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0so... (S) 2 e^2x would equal just e^2x does that help out?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0our exponent here (.8.06t) derives to: .06 right? so we need to modify this set up to include an (.06) without actually changing the value of the set up... what number can we multiply ANY number by to get the same value back? x times ? equals x ??

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0d (e^x) dx  =  e^x dx dx Or to right it another way: Dx(e^x) > Dx e^x Dx(e^7x) > Dx(7x) e^7x > 7 e^7x right>

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0not sure im getting the last part

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0ok.... tell me what your having difficulites with and I can help iron out the wrinkles :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok the (.8.06t) not getting the dirivitive of this

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0im thinking it involves the chain rule...which I think should be called the "gear"rule...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0I want you to think of a box of gears that are all meshed together so that when you turn the very first one, it has an effect on all the rest of them. each gear in turn is turning another correct?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes i understand how you get the .06 is this where we use the [15,0]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0not yet, we havent gotten to our initial function yet, we still need to find a way to get there first.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0we have a function: e^u that depends on "u" for its value right? u = .8 .06t and so the value of "u" depends on the value of "t" right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0why did we substititute?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0we substitued values to see how the original function behaves. What we need in order to integrate this original function is to modify the way it looks without changing its "value". we can easily integrate the function Du e^u to get e^u so this is our goal. We need to modify the "shape" of our original function so that it matches the "easy to integrate" function without changing the "value" of our original function.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0what number do we know of that is used to obtain the same "value" but a different "shape" of a function? x times ? = x ??

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0for example: say you only have a 20 dollar bill, and you want to buy some bubble gum for 1.00 but the cashier has no change to plit your $20. How can you purchase the bubble gum? by changing your $20 into a bunch of $1 bills... that is all we are wanting to do here.... so that we can make life easier for us

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0We have e^u we WANT Du e^u what value does Du have to be?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0Du is probably a bad name for that.... let me ask this.. what do we have to multiply (e^u) by in order to keep the same "value" e^u times ____ = e^u ?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0think 1....think 1.... 1 times e^u = e^u right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0does (.06)/(.06) = 1 ??

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0.06 e^.05 (S)  e^(.8 .06t) dt .06 look close to what we want it to be?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0if your unsure, tell me what your doubts are.... cause I can be rather stupid at times and mess alot of simple things up :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0in essense, we want to slide that bottom (.06) out of the way since it is a constant we can do that and put it under the left side. that leaves the integrand to be (e^.05)/.06 [S] .06 e^(.8.06t) dt > e^(.8.06t) F(t) =  [(e^.05)/.06] [e^(.8.06t)]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0or put another way:  e^(.85  .06t) F(t) =  .06

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0(Constants) [S] Du e^u du becomes (Constants) (e^u) is all we did in a nutshell

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0I gotta head to class for the next few hours... if your still lost, go ahead and post it for everyone to see :) Ciao
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