May 8th, 2016, 05:10 AM  #1 
Member Joined: Apr 2016 From: Hell Posts: 39 Thanks: 0  How to find the exponent of antiderivative? Imgur: The most awesome images on the Internet I don't understand the explanations in the text. How would this problem be solved? Also, what is the term for the stylized f? 
May 8th, 2016, 05:16 AM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,790 Thanks: 630 Math Focus: Yet to find out. 
The stylized f? You mean the integral sign? $\displaystyle \int$ Do you know what an antiderivative is? 
May 8th, 2016, 05:22 AM  #3 
Member Joined: Apr 2016 From: Hell Posts: 39 Thanks: 0  
May 8th, 2016, 05:32 AM  #4 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,790 Thanks: 630 Math Focus: Yet to find out. 
As a simple example, consider $\displaystyle y = x^2$ The derivative would be, $\displaystyle \frac{dy}{dx} = 2x^{21}$ Conversely, $\displaystyle \int{2x} dx = \frac{2x^{1+1}}{2} + C$ But I'm guessing this won't help you, as there's quite a bit going on behind the scenes. As I've mentioned before, this isn't a pattern matching game, you have to understand it first. Last edited by skipjack; May 8th, 2016 at 09:10 AM. 
May 8th, 2016, 05:44 AM  #5 
Member Joined: Apr 2016 From: Hell Posts: 39 Thanks: 0  
May 8th, 2016, 05:49 AM  #6 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,790 Thanks: 630 Math Focus: Yet to find out. 
I should have expressed it in general form, sorry. That way you can see what the definition is. I'm not on a device capable of using latex currently (at least not conveniently), so I will redirect you to a website. www.mathsisfun.com/calculus/integrationintroduction.html I think this is a reasonable, and fairly simple introduction. I suggest that you read through it, and take some notes. Last edited by skipjack; May 8th, 2016 at 09:17 AM. 
May 9th, 2016, 11:56 PM  #7 
Member Joined: Apr 2016 From: Hell Posts: 39 Thanks: 0 
How would anti differentiating work for negative exponents? $6x^{2} + 2x^{4} 3x^{3}$. How would the anti diff process work for fractions? I have $\frac{1}{6x^2}$ for the first part. Am I supposed to add one to x, and then put it all over 3? How would the fraction then resolve? 
May 10th, 2016, 12:30 AM  #8 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,790 Thanks: 630 Math Focus: Yet to find out. 
It works the same way. $\displaystyle \int{x^n}{dx} = \frac{1}{n+1} x^{n+1}$ But be careful of the case when you have $\displaystyle x^{1}$ $\displaystyle \int\frac{1}{x}{dx} = \int{x^{1}}{dx} = lnx$ Does this help? Also note that.. $\displaystyle \frac{1}{6x^2} â‰ 6x^{2}$ Last edited by Joppy; May 10th, 2016 at 12:36 AM. 
May 10th, 2016, 01:47 AM  #9  
Member Joined: Apr 2016 From: Hell Posts: 39 Thanks: 0  Quote:
 
May 10th, 2016, 03:47 AM  #10  
Senior Member Joined: Feb 2016 From: Australia Posts: 1,790 Thanks: 630 Math Focus: Yet to find out.  Quote:
$\displaystyle \int{x^n}dx = \frac{1}{n+1}x^{n+1}$ Let's apply this to your problem. $\displaystyle \int{\frac{x^{2}}{6}}dx$ (we can take constants outside of the integral sign here, so lets do that to tidy things up). $\displaystyle \frac{1}{6}\int{x^{2}}dx$ Now look at the rule i've provided at the top, can you identify n? It's 2 would you agree? That is, n = 2. Now let's substitute this back into the expression above, we have, $\displaystyle \int{x^n}dx = \frac{1}{n+1}x^{n+1}$ now substitute n, $\displaystyle \frac{1}{6}\int{x^{2}}dx = \frac{1}{2+1}x^{2+1} = \frac{1}{6x} $ Do you think you could apply a similar procedure to a different problem? Have a go integrating 2x^4 Last edited by Joppy; May 10th, 2016 at 04:10 AM.  

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