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Find \(\displaystyle \int\limits_{-7}^{-4} \left(- 3 x - 2\right)\, dx\).
The indefinite integtal is \(\displaystyle F(x)=- \frac{3 x^{2}}{2} - 2 x+C\). Using the Fundamental Theorem of Calculus Part II gives \(\displaystyle F(-4)-F(-7)=\left(-16\right)-\left(- \frac{119}{2}\right) = \frac{87}{2}\).
\begin{question}Find $\int\limits_{-7}^{-4} \left(- 3 x - 2\right)\, dx$. \soln{9cm}{The indefinite integtal is $F(x)=- \frac{3 x^{2}}{2} - 2 x+C$. Using the Fundamental Theorem of Calculus Part II gives $F(-4)-F(-7)=\left(-16\right)-\left(- \frac{119}{2}\right) = \frac{87}{2}$. } \end{question}
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<p> <p>Find <img class="equation_image" title=" \displaystyle \int\limits_{-7}^{-4} \left(- 3 x - 2\right)\, dx " src="/equation_images/%20%5Cdisplaystyle%20%5Cint%5Climits_%7B-7%7D%5E%7B-4%7D%20%5Cleft%28-%203%20x%20-%202%5Cright%29%5C%2C%20dx%20" alt="LaTeX: \displaystyle \int\limits_{-7}^{-4} \left(- 3 x - 2\right)\, dx " data-equation-content=" \displaystyle \int\limits_{-7}^{-4} \left(- 3 x - 2\right)\, dx " /> . </p> </p>
<p> <p>The indefinite integtal is <img class="equation_image" title=" \displaystyle F(x)=- \frac{3 x^{2}}{2} - 2 x+C " src="/equation_images/%20%5Cdisplaystyle%20F%28x%29%3D-%20%5Cfrac%7B3%20x%5E%7B2%7D%7D%7B2%7D%20-%202%20x%2BC%20" alt="LaTeX: \displaystyle F(x)=- \frac{3 x^{2}}{2} - 2 x+C " data-equation-content=" \displaystyle F(x)=- \frac{3 x^{2}}{2} - 2 x+C " /> . Using the Fundamental Theorem of Calculus Part II gives <img class="equation_image" title=" \displaystyle F(-4)-F(-7)=\left(-16\right)-\left(- \frac{119}{2}\right) = \frac{87}{2} " src="/equation_images/%20%5Cdisplaystyle%20F%28-4%29-F%28-7%29%3D%5Cleft%28-16%5Cright%29-%5Cleft%28-%20%5Cfrac%7B119%7D%7B2%7D%5Cright%29%20%3D%20%5Cfrac%7B87%7D%7B2%7D%20" alt="LaTeX: \displaystyle F(-4)-F(-7)=\left(-16\right)-\left(- \frac{119}{2}\right) = \frac{87}{2} " data-equation-content=" \displaystyle F(-4)-F(-7)=\left(-16\right)-\left(- \frac{119}{2}\right) = \frac{87}{2} " /> . </p> </p>