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Questions: Algebra BusinessCalculus
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Find \(\displaystyle \int\limits_{-8}^{0} \left(1 - 7 x\right)\, dx\).
The indefinite integtal is \(\displaystyle F(x)=- \frac{7 x^{2}}{2} + x+C\). Using the Fundamental Theorem of Calculus Part II gives \(\displaystyle F(0)-F(-8)=\left(0\right)-\left(-232\right) = 232\).
\begin{question}Find $\int\limits_{-8}^{0} \left(1 - 7 x\right)\, dx$.
\soln{9cm}{The indefinite integtal is $F(x)=- \frac{7 x^{2}}{2} + x+C$. Using the Fundamental Theorem of Calculus Part II gives $F(0)-F(-8)=\left(0\right)-\left(-232\right) = 232$. }
\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}^{0} \left(1 - 7 x\right)\, dx " src="/equation_images/%20%5Cdisplaystyle%20%5Cint%5Climits_%7B-8%7D%5E%7B0%7D%20%5Cleft%281%20-%207%20x%5Cright%29%5C%2C%20dx%20" alt="LaTeX: \displaystyle \int\limits_{-8}^{0} \left(1 - 7 x\right)\, dx " data-equation-content=" \displaystyle \int\limits_{-8}^{0} \left(1 - 7 x\right)\, dx " /> . </p> </p><p> <p>The indefinite integtal is <img class="equation_image" title=" \displaystyle F(x)=- \frac{7 x^{2}}{2} + x+C " src="/equation_images/%20%5Cdisplaystyle%20F%28x%29%3D-%20%5Cfrac%7B7%20x%5E%7B2%7D%7D%7B2%7D%20%2B%20x%2BC%20" alt="LaTeX: \displaystyle F(x)=- \frac{7 x^{2}}{2} + x+C " data-equation-content=" \displaystyle F(x)=- \frac{7 x^{2}}{2} + x+C " /> . Using the Fundamental Theorem of Calculus Part II gives <img class="equation_image" title=" \displaystyle F(0)-F(-8)=\left(0\right)-\left(-232\right) = 232 " src="/equation_images/%20%5Cdisplaystyle%20F%280%29-F%28-8%29%3D%5Cleft%280%5Cright%29-%5Cleft%28-232%5Cright%29%20%3D%20232%20" alt="LaTeX: \displaystyle F(0)-F(-8)=\left(0\right)-\left(-232\right) = 232 " data-equation-content=" \displaystyle F(0)-F(-8)=\left(0\right)-\left(-232\right) = 232 " /> . </p> </p>