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Questions: Algebra BusinessCalculus
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Find \(\displaystyle \int\limits_{8}^{11} \left(4 x^{3} - 4 x^{2} - 5 x - 7\right)\, dx\).
The indefinite integtal is \(\displaystyle F(x)=x^{4} - \frac{4 x^{3}}{3} - \frac{5 x^{2}}{2} - 7 x+C\). Using the Fundamental Theorem of Calculus Part II gives \(\displaystyle F(11)-F(8)=\left(\frac{74921}{6}\right)-\left(\frac{9592}{3}\right) = \frac{18579}{2}\).
\begin{question}Find $\int\limits_{8}^{11} \left(4 x^{3} - 4 x^{2} - 5 x - 7\right)\, dx$.
\soln{9cm}{The indefinite integtal is $F(x)=x^{4} - \frac{4 x^{3}}{3} - \frac{5 x^{2}}{2} - 7 x+C$. Using the Fundamental Theorem of Calculus Part II gives $F(11)-F(8)=\left(\frac{74921}{6}\right)-\left(\frac{9592}{3}\right) = \frac{18579}{2}$. }
\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}^{11} \left(4 x^{3} - 4 x^{2} - 5 x - 7\right)\, dx " src="/equation_images/%20%5Cdisplaystyle%20%5Cint%5Climits_%7B8%7D%5E%7B11%7D%20%5Cleft%284%20x%5E%7B3%7D%20-%204%20x%5E%7B2%7D%20-%205%20x%20-%207%5Cright%29%5C%2C%20dx%20" alt="LaTeX: \displaystyle \int\limits_{8}^{11} \left(4 x^{3} - 4 x^{2} - 5 x - 7\right)\, dx " data-equation-content=" \displaystyle \int\limits_{8}^{11} \left(4 x^{3} - 4 x^{2} - 5 x - 7\right)\, dx " /> . </p> </p><p> <p>The indefinite integtal is <img class="equation_image" title=" \displaystyle F(x)=x^{4} - \frac{4 x^{3}}{3} - \frac{5 x^{2}}{2} - 7 x+C " src="/equation_images/%20%5Cdisplaystyle%20F%28x%29%3Dx%5E%7B4%7D%20-%20%5Cfrac%7B4%20x%5E%7B3%7D%7D%7B3%7D%20-%20%5Cfrac%7B5%20x%5E%7B2%7D%7D%7B2%7D%20-%207%20x%2BC%20" alt="LaTeX: \displaystyle F(x)=x^{4} - \frac{4 x^{3}}{3} - \frac{5 x^{2}}{2} - 7 x+C " data-equation-content=" \displaystyle F(x)=x^{4} - \frac{4 x^{3}}{3} - \frac{5 x^{2}}{2} - 7 x+C " /> . Using the Fundamental Theorem of Calculus Part II gives <img class="equation_image" title=" \displaystyle F(11)-F(8)=\left(\frac{74921}{6}\right)-\left(\frac{9592}{3}\right) = \frac{18579}{2} " src="/equation_images/%20%5Cdisplaystyle%20F%2811%29-F%288%29%3D%5Cleft%28%5Cfrac%7B74921%7D%7B6%7D%5Cright%29-%5Cleft%28%5Cfrac%7B9592%7D%7B3%7D%5Cright%29%20%3D%20%5Cfrac%7B18579%7D%7B2%7D%20" alt="LaTeX: \displaystyle F(11)-F(8)=\left(\frac{74921}{6}\right)-\left(\frac{9592}{3}\right) = \frac{18579}{2} " data-equation-content=" \displaystyle F(11)-F(8)=\left(\frac{74921}{6}\right)-\left(\frac{9592}{3}\right) = \frac{18579}{2} " /> . </p> </p>