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Questions: Algebra BusinessCalculus
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Find \(\displaystyle \int\limits_{-1}^{7} \left(- x^{4} - 9 x^{3} - 2 x^{2} - 2 x + 3\right)\, dx\).
The indefinite integtal is \(\displaystyle F(x)=- \frac{x^{5}}{5} - \frac{9 x^{4}}{4} - \frac{2 x^{3}}{3} - x^{2} + 3 x+C\). Using the Fundamental Theorem of Calculus Part II gives \(\displaystyle F(7)-F(-1)=\left(- \frac{541219}{60}\right)-\left(- \frac{323}{60}\right) = - \frac{135224}{15}\).
\begin{question}Find $\int\limits_{-1}^{7} \left(- x^{4} - 9 x^{3} - 2 x^{2} - 2 x + 3\right)\, dx$.
\soln{9cm}{The indefinite integtal is $F(x)=- \frac{x^{5}}{5} - \frac{9 x^{4}}{4} - \frac{2 x^{3}}{3} - x^{2} + 3 x+C$. Using the Fundamental Theorem of Calculus Part II gives $F(7)-F(-1)=\left(- \frac{541219}{60}\right)-\left(- \frac{323}{60}\right) = - \frac{135224}{15}$. }
\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_{-1}^{7} \left(- x^{4} - 9 x^{3} - 2 x^{2} - 2 x + 3\right)\, dx " src="/equation_images/%20%5Cdisplaystyle%20%5Cint%5Climits_%7B-1%7D%5E%7B7%7D%20%5Cleft%28-%20x%5E%7B4%7D%20-%209%20x%5E%7B3%7D%20-%202%20x%5E%7B2%7D%20-%202%20x%20%2B%203%5Cright%29%5C%2C%20dx%20" alt="LaTeX: \displaystyle \int\limits_{-1}^{7} \left(- x^{4} - 9 x^{3} - 2 x^{2} - 2 x + 3\right)\, dx " data-equation-content=" \displaystyle \int\limits_{-1}^{7} \left(- x^{4} - 9 x^{3} - 2 x^{2} - 2 x + 3\right)\, dx " /> . </p> </p><p> <p>The indefinite integtal is <img class="equation_image" title=" \displaystyle F(x)=- \frac{x^{5}}{5} - \frac{9 x^{4}}{4} - \frac{2 x^{3}}{3} - x^{2} + 3 x+C " src="/equation_images/%20%5Cdisplaystyle%20F%28x%29%3D-%20%5Cfrac%7Bx%5E%7B5%7D%7D%7B5%7D%20-%20%5Cfrac%7B9%20x%5E%7B4%7D%7D%7B4%7D%20-%20%5Cfrac%7B2%20x%5E%7B3%7D%7D%7B3%7D%20-%20x%5E%7B2%7D%20%2B%203%20x%2BC%20" alt="LaTeX: \displaystyle F(x)=- \frac{x^{5}}{5} - \frac{9 x^{4}}{4} - \frac{2 x^{3}}{3} - x^{2} + 3 x+C " data-equation-content=" \displaystyle F(x)=- \frac{x^{5}}{5} - \frac{9 x^{4}}{4} - \frac{2 x^{3}}{3} - x^{2} + 3 x+C " /> . Using the Fundamental Theorem of Calculus Part II gives <img class="equation_image" title=" \displaystyle F(7)-F(-1)=\left(- \frac{541219}{60}\right)-\left(- \frac{323}{60}\right) = - \frac{135224}{15} " src="/equation_images/%20%5Cdisplaystyle%20F%287%29-F%28-1%29%3D%5Cleft%28-%20%5Cfrac%7B541219%7D%7B60%7D%5Cright%29-%5Cleft%28-%20%5Cfrac%7B323%7D%7B60%7D%5Cright%29%20%3D%20-%20%5Cfrac%7B135224%7D%7B15%7D%20" alt="LaTeX: \displaystyle F(7)-F(-1)=\left(- \frac{541219}{60}\right)-\left(- \frac{323}{60}\right) = - \frac{135224}{15} " data-equation-content=" \displaystyle F(7)-F(-1)=\left(- \frac{541219}{60}\right)-\left(- \frac{323}{60}\right) = - \frac{135224}{15} " /> . </p> </p>