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anonymous
 5 years ago
use the limit definition to evaluate the integral of (e^x3)dx upper limit is 3, lower limit 1.
anonymous
 5 years ago
use the limit definition to evaluate the integral of (e^x3)dx upper limit is 3, lower limit 1.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0let x3 =t dx=dt hence our integral becomes \[\int\limits_{1}^{3}e ^{t}dt\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the question is Evaluate using the limit definition, \[\int\limits_{1}^{3}(e^x3)dx\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0maybe a mistake here. If you change from x  3 to t you have to change the limits of integration. if x = 1 then t = 13 = 2 and if x = 3 then t = 33 = 0 so integral should be \[\int^0_{2} e^t,dt\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oops Thought it was \[e^{x3}\] not \[e^x3\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Are you really being asked to use a Reimann sum?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0is there a way to solve this without using reimann sum? do u have to take the natural log of e^x?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0int(e^x3) =int(e^x)int(3) =e^x3x+C C is a constant

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hey could this be the final answer? u didnt use reimanns sum though

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0well you also have the limits too this is alot easier than reimann sums it would be easy to do the reimann sums on int(3) but int(e^x) not sure never even tried to use riemann sum for that one

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0int(e^x3,x=3..1) =(e^x3x,x=3..1) =(e^33(3))(e^11(1)) thats the answer you can simplify of course

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0oops mistake =(e^33(3))(e^13(1))

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0i have to go good luck

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0holy moly. i see no way to compute this reimann sum because we do not have a summation formula for this. the integral is easy enough: \[\int^3_1e^x,dx=e^33\] \[\int^3_1 3,dx=6\] since it is a constant and the length of the path is 2. so answer is \[e^3e6\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0could you please explain further?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sure. We want a definite integral. Easy way is to find the antiderivative, plug in the upper limit, the lower limit, and subtract. It is easy to find the antiderivative of \[e^x\] since it is its own derivative. so \[\int e^x,dx = e^x\] evaluate at 3 get \[e^3\] evaluate at 1 get \[e\] subtract and get \[e^3e\] now 3 is a constant. a horizontal line. So the integral is just base times hight. the hight is 3, the base is the length from 1 to 3 which is 2, and 3*2=6. I am ignoring the "" because i am just going to subtract.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i guess hight is spelled with an e as height. not that literate today. you could also find this integral by taking the antiderivative: \[\int 3 dx = 3x\] plug in 3 get 9. plug in 1 get 3. subtract get 6. but this is a waste of time, because the integral of a constant is always constant times length of path. \[\int^b_a c dx=(ba)c\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no problem but i still have no idea how to compute this as a reimann sum

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0see if this helps its a geometric series

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0but maybe there is a mistake somewhere but i'm on the right track

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0use l'hospital's rule and you have \[\lim_{u \rightarrow 0} \frac{ue^u}{1e^{u}}=\lim_{u \rightarrow 0} \frac{e^u+ue^{u}}{e^{u}}\]

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0\[=\lim_{u \rightarrow 0} \frac{1+u}{1}=\lim_{u \rightarrow 0} (1u)=10=1\]

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0and (1)(ee^3)=e^3e :) and we win!
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