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 450081592 January 18th, 2010 04:08 PM

Find area

Find the area between the graph of f and the x-axis.

$f(x)= x^3 + 1, x\in [-2, -1].$

$\int _{-2}\,^{-1}\!x^3+1dt$

 Erebos January 18th, 2010 04:14 PM

Re: Find area

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

 450081592 January 18th, 2010 04:37 PM

Re: Find area

Quote:
 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 $1/4x^4 + x$

 billymac00 January 18th, 2010 05:15 PM

Re: Find area

well, Wolframalpha gives -11/4 ...

 450081592 January 18th, 2010 05:19 PM

Re: Find area

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

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

 aswoods January 18th, 2010 05:21 PM

Re: Find area

$\int_{-2}^{-1}x^3+1 dx= \left[ \frac14 x^4+x \right]_{-2}^{-1} = (\frac14 (-1)^4 - 1) - (\frac14 (-2)^4 - 2) = (-\frac34)-(2) = -\frac{11}{4}$

 greg1313 January 18th, 2010 05:25 PM

Didn't see the above.

 skipjack January 19th, 2010 02:45 AM

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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