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May 11th, 2016, 02:53 AM   #11
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 Originally Posted by Joppy Ok let's try work through it, see this rule here, $\displaystyle \int{x^n}dx = \frac{1}{n+1}x^{n+1}$ 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
Is that -6x^-3

How does anti differentiating work for questions with ln and e?

I'm reviewing the practice sheet for the final exam. One question is: True or false: antidifferention of 1/2x times dx = ln x^2 + C.

What does the ln mean? Does it just represent 1/2/1, so 2? Tags antiderivative, exponent, find Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Shamieh Calculus 1 November 3rd, 2013 06:59 PM mortified_penguin Calculus 7 January 24th, 2013 08:03 AM Valar30 Calculus 2 November 15th, 2010 11:58 AM Valar30 Calculus 1 November 15th, 2010 09:03 AM lovetolearn Algebra 1 December 31st, 1969 04:00 PM

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