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Questions: Algebra BusinessCalculus
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Find \(\displaystyle \int\limits_{-8}^{-2} \left(x^{4} - 6 x^{3} + 8 x^{2} - 5 x - 5\right)\, dx\).
The indefinite integtal is \(\displaystyle F(x)=\frac{x^{5}}{5} - \frac{3 x^{4}}{2} + \frac{8 x^{3}}{3} - \frac{5 x^{2}}{2} - 5 x+C\). Using the Fundamental Theorem of Calculus Part II gives \(\displaystyle F(-2)-F(-8)=\left(- \frac{776}{15}\right)-\left(- \frac{212744}{15}\right) = \frac{70656}{5}\).
\begin{question}Find $\int\limits_{-8}^{-2} \left(x^{4} - 6 x^{3} + 8 x^{2} - 5 x - 5\right)\, dx$.
\soln{9cm}{The indefinite integtal is $F(x)=\frac{x^{5}}{5} - \frac{3 x^{4}}{2} + \frac{8 x^{3}}{3} - \frac{5 x^{2}}{2} - 5 x+C$. Using the Fundamental Theorem of Calculus Part II gives $F(-2)-F(-8)=\left(- \frac{776}{15}\right)-\left(- \frac{212744}{15}\right) = \frac{70656}{5}$. }
\end{question}
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\begin{document}\begin{question}(10pts) The question goes here!
\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Find <img class="equation_image" title=" \displaystyle \int\limits_{-8}^{-2} \left(x^{4} - 6 x^{3} + 8 x^{2} - 5 x - 5\right)\, dx " src="/equation_images/%20%5Cdisplaystyle%20%5Cint%5Climits_%7B-8%7D%5E%7B-2%7D%20%5Cleft%28x%5E%7B4%7D%20-%206%20x%5E%7B3%7D%20%2B%208%20x%5E%7B2%7D%20-%205%20x%20-%205%5Cright%29%5C%2C%20dx%20" alt="LaTeX: \displaystyle \int\limits_{-8}^{-2} \left(x^{4} - 6 x^{3} + 8 x^{2} - 5 x - 5\right)\, dx " data-equation-content=" \displaystyle \int\limits_{-8}^{-2} \left(x^{4} - 6 x^{3} + 8 x^{2} - 5 x - 5\right)\, dx " /> . </p> </p><p> <p>The indefinite integtal is <img class="equation_image" title=" \displaystyle F(x)=\frac{x^{5}}{5} - \frac{3 x^{4}}{2} + \frac{8 x^{3}}{3} - \frac{5 x^{2}}{2} - 5 x+C " src="/equation_images/%20%5Cdisplaystyle%20F%28x%29%3D%5Cfrac%7Bx%5E%7B5%7D%7D%7B5%7D%20-%20%5Cfrac%7B3%20x%5E%7B4%7D%7D%7B2%7D%20%2B%20%5Cfrac%7B8%20x%5E%7B3%7D%7D%7B3%7D%20-%20%5Cfrac%7B5%20x%5E%7B2%7D%7D%7B2%7D%20-%205%20x%2BC%20" alt="LaTeX: \displaystyle F(x)=\frac{x^{5}}{5} - \frac{3 x^{4}}{2} + \frac{8 x^{3}}{3} - \frac{5 x^{2}}{2} - 5 x+C " data-equation-content=" \displaystyle F(x)=\frac{x^{5}}{5} - \frac{3 x^{4}}{2} + \frac{8 x^{3}}{3} - \frac{5 x^{2}}{2} - 5 x+C " /> . Using the Fundamental Theorem of Calculus Part II gives <img class="equation_image" title=" \displaystyle F(-2)-F(-8)=\left(- \frac{776}{15}\right)-\left(- \frac{212744}{15}\right) = \frac{70656}{5} " src="/equation_images/%20%5Cdisplaystyle%20F%28-2%29-F%28-8%29%3D%5Cleft%28-%20%5Cfrac%7B776%7D%7B15%7D%5Cright%29-%5Cleft%28-%20%5Cfrac%7B212744%7D%7B15%7D%5Cright%29%20%3D%20%5Cfrac%7B70656%7D%7B5%7D%20" alt="LaTeX: \displaystyle F(-2)-F(-8)=\left(- \frac{776}{15}\right)-\left(- \frac{212744}{15}\right) = \frac{70656}{5} " data-equation-content=" \displaystyle F(-2)-F(-8)=\left(- \frac{776}{15}\right)-\left(- \frac{212744}{15}\right) = \frac{70656}{5} " /> . </p> </p>