Answer
$-10/3$
Work Step by Step
Original Equation: $\int$ $(x^{2}-3)dx$ on the interval $[3,-2]$
To solve this integral, we first need to find the anti-derivative.
The anti-derivative of $x^{n}$ is found through the equation $\frac{x^{n+1}}{n+1}$. by applying this formula to each term in the equation, we see that the final anti-derivative is $\frac{x^{3}}{3}-3x$
Now that we have this equation, we simply subtract the bottom range from the upper range. Our range is $[3,-2]$, so we plug 3 and -2 into the anti derivative and the difference of the two is our final answer.
$(\frac{3^{3}}{3}-3(3))$-$(\frac{-2^{3}}{3}-3(-2))$ $= \frac{-10}{3}$
