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Questions: Algebra BusinessCalculus
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Find \(\displaystyle \int\limits_{4}^{9} \left(x^{3} - 3 x^{2} - x - 2\right)\, dx\).
The indefinite integtal is \(\displaystyle F(x)=\frac{x^{4}}{4} - x^{3} - \frac{x^{2}}{2} - 2 x+C\). Using the Fundamental Theorem of Calculus Part II gives \(\displaystyle F(9)-F(4)=\left(\frac{3411}{4}\right)-\left(-16\right) = \frac{3475}{4}\).
\begin{question}Find $\int\limits_{4}^{9} \left(x^{3} - 3 x^{2} - x - 2\right)\, dx$.
\soln{9cm}{The indefinite integtal is $F(x)=\frac{x^{4}}{4} - x^{3} - \frac{x^{2}}{2} - 2 x+C$. Using the Fundamental Theorem of Calculus Part II gives $F(9)-F(4)=\left(\frac{3411}{4}\right)-\left(-16\right) = \frac{3475}{4}$. }
\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_{4}^{9} \left(x^{3} - 3 x^{2} - x - 2\right)\, dx " src="/equation_images/%20%5Cdisplaystyle%20%5Cint%5Climits_%7B4%7D%5E%7B9%7D%20%5Cleft%28x%5E%7B3%7D%20-%203%20x%5E%7B2%7D%20-%20x%20-%202%5Cright%29%5C%2C%20dx%20" alt="LaTeX: \displaystyle \int\limits_{4}^{9} \left(x^{3} - 3 x^{2} - x - 2\right)\, dx " data-equation-content=" \displaystyle \int\limits_{4}^{9} \left(x^{3} - 3 x^{2} - x - 2\right)\, dx " /> . </p> </p><p> <p>The indefinite integtal is <img class="equation_image" title=" \displaystyle F(x)=\frac{x^{4}}{4} - x^{3} - \frac{x^{2}}{2} - 2 x+C " src="/equation_images/%20%5Cdisplaystyle%20F%28x%29%3D%5Cfrac%7Bx%5E%7B4%7D%7D%7B4%7D%20-%20x%5E%7B3%7D%20-%20%5Cfrac%7Bx%5E%7B2%7D%7D%7B2%7D%20-%202%20x%2BC%20" alt="LaTeX: \displaystyle F(x)=\frac{x^{4}}{4} - x^{3} - \frac{x^{2}}{2} - 2 x+C " data-equation-content=" \displaystyle F(x)=\frac{x^{4}}{4} - x^{3} - \frac{x^{2}}{2} - 2 x+C " /> . Using the Fundamental Theorem of Calculus Part II gives <img class="equation_image" title=" \displaystyle F(9)-F(4)=\left(\frac{3411}{4}\right)-\left(-16\right) = \frac{3475}{4} " src="/equation_images/%20%5Cdisplaystyle%20F%289%29-F%284%29%3D%5Cleft%28%5Cfrac%7B3411%7D%7B4%7D%5Cright%29-%5Cleft%28-16%5Cright%29%20%3D%20%5Cfrac%7B3475%7D%7B4%7D%20" alt="LaTeX: \displaystyle F(9)-F(4)=\left(\frac{3411}{4}\right)-\left(-16\right) = \frac{3475}{4} " data-equation-content=" \displaystyle F(9)-F(4)=\left(\frac{3411}{4}\right)-\left(-16\right) = \frac{3475}{4} " /> . </p> </p>