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bettyboop8904
 3 years 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.
bettyboop8904
 3 years 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.

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bettyboop8904
 3 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{1} (9x ^{e}+e ^{x})dx\] Do I use u substitution?

CanadianAsian
 3 years ago
Best ResponseYou've already chosen the best response.2I 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.

CanadianAsian
 3 years ago
Best ResponseYou've already chosen the best response.2The 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

bettyboop8904
 3 years ago
Best ResponseYou've already chosen the best response.0Wait I'm confused on the last post. \[\frac{ x ^{n+1} }{ n+1 }\] Isn't that the antiderivative?

bettyboop8904
 3 years ago
Best ResponseYou've already chosen the best response.0is that what an integral is?

CanadianAsian
 3 years ago
Best ResponseYou've already chosen the best response.2Exactly! An integral is the antiderivative.

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

CanadianAsian
 3 years ago
Best ResponseYou've already chosen the best response.2Well 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.

bettyboop8904
 3 years ago
Best ResponseYou've already chosen the best response.0Oh 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?

bettyboop8904
 3 years ago
Best ResponseYou've already chosen the best response.0so does that mean you would have: \[\frac{ 9x ^{e+1} }{ e+1 }\] and \[\frac{ e ^{x+1} }{ x+1 }\] is that right?

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

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

bettyboop8904
 3 years ago
Best ResponseYou've already chosen the best response.0oh yeah that's right because the integral of e^x is itself right?

bettyboop8904
 3 years ago
Best ResponseYou've already chosen the best response.0Ok so what's next? or is that all I have to do with it?

bettyboop8904
 3 years ago
Best ResponseYou've already chosen the best response.0It just says evaluate the integral

CanadianAsian
 3 years ago
Best ResponseYou've already chosen the best response.2Once 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.

bettyboop8904
 3 years ago
Best ResponseYou've already chosen the best response.0Oh wait I just realized I typed the problem out. There is no 9 in front of the x^e

bettyboop8904
 3 years ago
Best ResponseYou've already chosen the best response.0*typed it out wrong lol

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

bettyboop8904
 3 years ago
Best ResponseYou've already chosen the best response.0stupid question how do you get e^1 from e^1e^0?

CanadianAsian
 3 years ago
Best ResponseYou've already chosen the best response.2so e^1 = e e^0 = 1 So e^1  e^0 = e  1

bettyboop8904
 3 years ago
Best ResponseYou've already chosen the best response.0oh 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
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