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 January 18th, 2010, 04:08 PM #1 Senior Member   Joined: Nov 2009 Posts: 169 Thanks: 0 Find area Find the area between the graph of f and the x-axis. $f(x)= x^3 + 1, x\in [-2, -1].$ $\int _{-2}\,^{-1}\!x^3+1dt$
 January 18th, 2010, 04:14 PM #2 Member   Joined: Dec 2009 Posts: 31 Thanks: 0 Re: Find area Just take the definite integral of f(x) from -2 to -1 (your final answer will be 11/3).
January 18th, 2010, 04:37 PM   #3
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Re: Find area

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 Originally Posted by Erebos Just take the definite integral of f(x) from -2 to -1 (your final answer will be 11/3).

I got 4/7 as my final answer, do I need a minus sign in front of the integral, the anti deritavitive I got is $1/4x^4 + x$

 January 18th, 2010, 05:15 PM #4 Senior Member   Joined: Aug 2008 From: Blacksburg VA USA Posts: 354 Thanks: 7 Math Focus: primes of course Re: Find area well, Wolframalpha gives -11/4 ...
January 18th, 2010, 05:19 PM   #5
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Re: Find area

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 Originally Posted by billymac00 well, Wolframalpha gives -11/4 ...

Can you show me how you got that, what is the anti derivative you got?

 January 18th, 2010, 05:21 PM #6 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 Re: Find area $\int_{-2}^{-1}x^3+1 dx= \left[ \frac14 x^4+x \right]_{-2}^{-1} = (\frac14 (-1)^4 - 1) - (\frac14 (-2)^4 - 2) = (-\frac34)-(2) = -\frac{11}{4}$
 January 18th, 2010, 05:25 PM #7 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond Didn't see the above.
January 19th, 2010, 02:45 AM   #8
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Quote:
 Originally Posted by 450081592 do I need a minus sign in front of the integral
The area lies entirely "below" the x-axis, so you should put a minus sign in front of the integral.

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