November 27th, 2014, 12:33 PM  #1 
Member Joined: Sep 2014 From: Cambridge Posts: 64 Thanks: 4  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 
November 27th, 2014, 01:11 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond 
In general, $\int_a^b f(x)\,dx=F(b)F(a)$, where $F$ is the antiderivative of $f$. $\displaystyle \int_{6}^3183xx^2\,dx=\left.\left(18x\frac32x^2\frac13x^3\right)\right_{6}^3=\left(54\frac{27}{2}9\right)(10854+72)=121.5$ Last edited by greg1313; December 2nd, 2014 at 05:37 AM. 

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