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November 27th, 2014, 12:33 PM   #1
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Fundamental Theorem

The area between y= 18 -3x -x^2 and the x axis


The answer I got was 202.5, is this correct?

I found the x values for when the function = 0 and got x = -6, x = 3.

Then I found the antiderivative of the function and plugged in x = 9 and got 202.5
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November 27th, 2014, 01:11 PM   #2
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In general, $\int_a^b f(x)\,dx=F(b)-F(a)$, where $F$ is the antiderivative of $f$.

$\displaystyle \int_{-6}^318-3x-x^2\,dx=\left.\left(18x-\frac32x^2-\frac13x^3\right)\right|_{-6}^3=\left(54-\frac{27}{2}-9\right)-(-108-54+72)=121.5$
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Last edited by greg1313; December 2nd, 2014 at 05:37 AM.
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