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Questions: Algebra BusinessCalculus
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Find \(\displaystyle \int\limits_{10}^{14} \left(6 x^{2} - 3 x - 3\right)\, dx\).
The indefinite integtal is \(\displaystyle F(x)=2 x^{3} - \frac{3 x^{2}}{2} - 3 x+C\). Using the Fundamental Theorem of Calculus Part II gives \(\displaystyle F(14)-F(10)=\left(5152\right)-\left(1820\right) = 3332\).
\begin{question}Find $\int\limits_{10}^{14} \left(6 x^{2} - 3 x - 3\right)\, dx$.
\soln{9cm}{The indefinite integtal is $F(x)=2 x^{3} - \frac{3 x^{2}}{2} - 3 x+C$. Using the Fundamental Theorem of Calculus Part II gives $F(14)-F(10)=\left(5152\right)-\left(1820\right) = 3332$. }
\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}^{14} \left(6 x^{2} - 3 x - 3\right)\, dx " src="/equation_images/%20%5Cdisplaystyle%20%5Cint%5Climits_%7B10%7D%5E%7B14%7D%20%5Cleft%286%20x%5E%7B2%7D%20-%203%20x%20-%203%5Cright%29%5C%2C%20dx%20" alt="LaTeX: \displaystyle \int\limits_{10}^{14} \left(6 x^{2} - 3 x - 3\right)\, dx " data-equation-content=" \displaystyle \int\limits_{10}^{14} \left(6 x^{2} - 3 x - 3\right)\, dx " /> . </p> </p><p> <p>The indefinite integtal is <img class="equation_image" title=" \displaystyle F(x)=2 x^{3} - \frac{3 x^{2}}{2} - 3 x+C " src="/equation_images/%20%5Cdisplaystyle%20F%28x%29%3D2%20x%5E%7B3%7D%20-%20%5Cfrac%7B3%20x%5E%7B2%7D%7D%7B2%7D%20-%203%20x%2BC%20" alt="LaTeX: \displaystyle F(x)=2 x^{3} - \frac{3 x^{2}}{2} - 3 x+C " data-equation-content=" \displaystyle F(x)=2 x^{3} - \frac{3 x^{2}}{2} - 3 x+C " /> . Using the Fundamental Theorem of Calculus Part II gives <img class="equation_image" title=" \displaystyle F(14)-F(10)=\left(5152\right)-\left(1820\right) = 3332 " src="/equation_images/%20%5Cdisplaystyle%20F%2814%29-F%2810%29%3D%5Cleft%285152%5Cright%29-%5Cleft%281820%5Cright%29%20%3D%203332%20" alt="LaTeX: \displaystyle F(14)-F(10)=\left(5152\right)-\left(1820\right) = 3332 " data-equation-content=" \displaystyle F(14)-F(10)=\left(5152\right)-\left(1820\right) = 3332 " /> . </p> </p>