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Can someone give me a quick recap of integrals? I have an example and there are 5 problems that are done similarly. Example is in the post with equation converter helper.
 one year ago
 one year ago
Can someone give me a quick recap of integrals? I have an example and there are 5 problems that are done similarly. Example is in the post with equation converter helper.
 one year ago
 one year ago

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bettyboop8904Best ResponseYou've already chosen the best response.0
\[\int\limits_{0}^{1} (9x ^{e}+e ^{x})dx\] Do I use u substitution?
 one year ago

CanadianAsianBest ResponseYou've already chosen the best response.2
I can't tell what the power of x is but it looks like an e? Either way, you can break this integral into two parts. \[\int\limits_{0}^{1}9x^e + \int\limits_{0}^{1}e^x\] Then just take integrate the individual integrals.
 one year ago

CanadianAsianBest ResponseYou've already chosen the best response.2
The rule of integration for X^n where n is a constant is \[x^{n+1}/(n+1)\] And the integral of e^x is just e^x
 one year ago

bettyboop8904Best ResponseYou've already chosen the best response.0
Wait I'm confused on the last post. \[\frac{ x ^{n+1} }{ n+1 }\] Isn't that the antiderivative?
 one year ago

bettyboop8904Best ResponseYou've already chosen the best response.0
is that what an integral is?
 one year ago

CanadianAsianBest ResponseYou've already chosen the best response.2
Exactly! An integral is the antiderivative.
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
recap of integrals ? try this.... http://openstudy.com/users/hartnn#/updates/50960518e4b0d0275a3ccfba
 one year ago

CanadianAsianBest ResponseYou've already chosen the best response.2
Well not exactly, but a key component of taking the integral of something is finding the antiderivative. If there are no bounds, then an integral is essentially the antiderivative.
 one year ago

bettyboop8904Best ResponseYou've already chosen the best response.0
Oh ok = ) So that's how you solve an integral. you use the rule that you can split the integrals up and then solve each one by finding the antiderivative. Oh yeah bc you have to incorporate the integral 0 to 1 right?
 one year ago

bettyboop8904Best ResponseYou've already chosen the best response.0
so does that mean you would have: \[\frac{ 9x ^{e+1} }{ e+1 }\] and \[\frac{ e ^{x+1} }{ x+1 }\] is that right?
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
the first part is correct, for e^x \(\int e^xdx=e^x+c\)
 one year ago

CanadianAsianBest ResponseYou've already chosen the best response.2
But since this is a definite integral (it has bounds) you can ignore the c, which will cancel out anyway.
 one year ago

bettyboop8904Best ResponseYou've already chosen the best response.0
oh yeah that's right because the integral of e^x is itself right?
 one year ago

bettyboop8904Best ResponseYou've already chosen the best response.0
Ok so what's next? or is that all I have to do with it?
 one year ago

bettyboop8904Best ResponseYou've already chosen the best response.0
It just says evaluate the integral
 one year ago

CanadianAsianBest ResponseYou've already chosen the best response.2
Once you've taken the antiderivative of it you plug in your bounds for x So for the integral of e^x for example: you'd get \[e^1  e^0\] Which simplifies into e1 But you have to remember that you're adding this to the integral of the first half.
 one year ago

bettyboop8904Best ResponseYou've already chosen the best response.0
Oh wait I just realized I typed the problem out. There is no 9 in front of the x^e
 one year ago

bettyboop8904Best ResponseYou've already chosen the best response.0
*typed it out wrong lol
 one year ago

CanadianAsianBest ResponseYou've already chosen the best response.2
The answer you posted above was correct for the antiderivative of x^e, just take out the 9 then.
 one year ago

bettyboop8904Best ResponseYou've already chosen the best response.0
stupid question how do you get e^1 from e^1e^0?
 one year ago

CanadianAsianBest ResponseYou've already chosen the best response.2
so e^1 = e e^0 = 1 So e^1  e^0 = e  1
 one year ago

bettyboop8904Best ResponseYou've already chosen the best response.0
oh ok I thought the 1 was the exponent of e from the rule of two bases being the same the exponents divide you know what I'm trying to say? lol
 one year ago
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