Area between 2 graphs

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April 10th 2010, 07:56 PM
Archduke01

Area between 2 graphs

Find the area enclosed between http://euler.vaniercollege.qc.ca/web...7f78a5a001.png and http://euler.vaniercollege.qc.ca/web...d9d094b661.png from http://euler.vaniercollege.qc.ca/web...e517fc5a21.png to http://euler.vaniercollege.qc.ca/web...c2c64b5631.png.

$\int_{-2}^{6} [(0.4^2+3) - (x)] dx$

$\frac {0.4x^3}{3} + 3x - \frac {x^2}{2}$

If I'm not mistaken, I now have to use the Fb - Fa formula. However, my answer turns out wrong so I'm assuming I made a mistake in the calculations shown above. Can someone please tell me where it is?
April 10th 2010, 08:07 PM
skeeter

Quote:

Originally Posted by Archduke01

Find the area enclosed between http://euler.vaniercollege.qc.ca/web...7f78a5a001.png and http://euler.vaniercollege.qc.ca/web...d9d094b661.png from http://euler.vaniercollege.qc.ca/web...e517fc5a21.png to http://euler.vaniercollege.qc.ca/web...c2c64b5631.png.

$\int_{-2}^{6} [(0.4^2+3) - (x)] dx$

$\frac {0.4x^3}{3} + 3x - \frac {x^2}{2}$

If I'm not mistaken, I now have to use the Fb - Fa formula. However, my answer turns out wrong so I'm assuming I made a mistake in the calculations shown above. Can someone please tell me where it is?

your antiderivative is correct ... error in evaluation from x = -2 to x = 6, maybe?
April 10th 2010, 08:14 PM
Archduke01

$\frac {0.4x^3}{3} + 3x - \frac {x^2}{2}$

$b = 6$
$\frac {0.4*6^3}{3} + 3*6 - \frac {6^2}{2} = 28.8$

$a = -2$
$<br /> \frac {0.4*(-2)^3}{3} + 3*(-2) - \frac {(-2)^2}{2} = -5.07$

$F(b) - F(a) = 28.8 - (-5.07) = 33.86$

I don't understand ... I've triple-checked, and I get the same answer every time. It's wrong.
April 10th 2010, 08:20 PM
skeeter

$\frac{0.4(-2)^3}{3} + 3(-2) - \frac{(-2)^2}{2}$

$\frac{0.4(-8)}{3} - 6 - \frac{4}{2}$

$\frac{-3.2}{3} - 6 - 2 = -9.0666...$