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Questions: Algebra BusinessCalculus
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Find \(\displaystyle \int\limits_{-10}^{-9} \left(4 x^{2} + 6 x - 4\right)\, dx\).
The indefinite integtal is \(\displaystyle F(x)=\frac{4 x^{3}}{3} + 3 x^{2} - 4 x+C\). Using the Fundamental Theorem of Calculus Part II gives \(\displaystyle F(-9)-F(-10)=\left(-693\right)-\left(- \frac{2980}{3}\right) = \frac{901}{3}\).
\begin{question}Find $\int\limits_{-10}^{-9} \left(4 x^{2} + 6 x - 4\right)\, dx$.
\soln{9cm}{The indefinite integtal is $F(x)=\frac{4 x^{3}}{3} + 3 x^{2} - 4 x+C$. Using the Fundamental Theorem of Calculus Part II gives $F(-9)-F(-10)=\left(-693\right)-\left(- \frac{2980}{3}\right) = \frac{901}{3}$. }
\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_{-10}^{-9} \left(4 x^{2} + 6 x - 4\right)\, dx " src="/equation_images/%20%5Cdisplaystyle%20%5Cint%5Climits_%7B-10%7D%5E%7B-9%7D%20%5Cleft%284%20x%5E%7B2%7D%20%2B%206%20x%20-%204%5Cright%29%5C%2C%20dx%20" alt="LaTeX: \displaystyle \int\limits_{-10}^{-9} \left(4 x^{2} + 6 x - 4\right)\, dx " data-equation-content=" \displaystyle \int\limits_{-10}^{-9} \left(4 x^{2} + 6 x - 4\right)\, dx " /> . </p> </p><p> <p>The indefinite integtal is <img class="equation_image" title=" \displaystyle F(x)=\frac{4 x^{3}}{3} + 3 x^{2} - 4 x+C " src="/equation_images/%20%5Cdisplaystyle%20F%28x%29%3D%5Cfrac%7B4%20x%5E%7B3%7D%7D%7B3%7D%20%2B%203%20x%5E%7B2%7D%20-%204%20x%2BC%20" alt="LaTeX: \displaystyle F(x)=\frac{4 x^{3}}{3} + 3 x^{2} - 4 x+C " data-equation-content=" \displaystyle F(x)=\frac{4 x^{3}}{3} + 3 x^{2} - 4 x+C " /> . Using the Fundamental Theorem of Calculus Part II gives <img class="equation_image" title=" \displaystyle F(-9)-F(-10)=\left(-693\right)-\left(- \frac{2980}{3}\right) = \frac{901}{3} " src="/equation_images/%20%5Cdisplaystyle%20F%28-9%29-F%28-10%29%3D%5Cleft%28-693%5Cright%29-%5Cleft%28-%20%5Cfrac%7B2980%7D%7B3%7D%5Cright%29%20%3D%20%5Cfrac%7B901%7D%7B3%7D%20" alt="LaTeX: \displaystyle F(-9)-F(-10)=\left(-693\right)-\left(- \frac{2980}{3}\right) = \frac{901}{3} " data-equation-content=" \displaystyle F(-9)-F(-10)=\left(-693\right)-\left(- \frac{2980}{3}\right) = \frac{901}{3} " /> . </p> </p>