\(\text{www.the}\beta\text{etafunction.com}\)
Home
Login
Questions: Algebra BusinessCalculus
Please login to create an exam or a quiz.
Find \(\displaystyle \int\limits_{6}^{12} \left(5 x^{3} + 5 x^{2} - 6 x + 8\right)\, dx\).
The indefinite integtal is \(\displaystyle F(x)=\frac{5 x^{4}}{4} + \frac{5 x^{3}}{3} - 3 x^{2} + 8 x+C\). Using the Fundamental Theorem of Calculus Part II gives \(\displaystyle F(12)-F(6)=\left(28464\right)-\left(1920\right) = 26544\).
\begin{question}Find $\int\limits_{6}^{12} \left(5 x^{3} + 5 x^{2} - 6 x + 8\right)\, dx$.
\soln{9cm}{The indefinite integtal is $F(x)=\frac{5 x^{4}}{4} + \frac{5 x^{3}}{3} - 3 x^{2} + 8 x+C$. Using the Fundamental Theorem of Calculus Part II gives $F(12)-F(6)=\left(28464\right)-\left(1920\right) = 26544$. }
\end{question}
\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage[margin=2cm]{geometry}
\usepackage{tcolorbox}
\newcounter{ExamNumber}
\newcounter{questioncount}
\stepcounter{questioncount}
\newenvironment{question}{{\noindent\bfseries Question \arabic{questioncount}.}}{\stepcounter{questioncount}}
\renewcommand{\labelenumi}{{\bfseries (\alph{enumi})}}
\newif\ifShowSolution
\newcommand{\soln}[2]{%
\ifShowSolution%
\noindent\begin{tcolorbox}[colframe=blue,title=Solution]#2\end{tcolorbox}\else%
\vspace{#1}%
\fi%
}%
\newcommand{\hideifShowSolution}[1]{%
\ifShowSolution%
%
\else%
#1%
\fi%
}%
\everymath{\displaystyle}
\ShowSolutiontrue
\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_{6}^{12} \left(5 x^{3} + 5 x^{2} - 6 x + 8\right)\, dx " src="/equation_images/%20%5Cdisplaystyle%20%5Cint%5Climits_%7B6%7D%5E%7B12%7D%20%5Cleft%285%20x%5E%7B3%7D%20%2B%205%20x%5E%7B2%7D%20-%206%20x%20%2B%208%5Cright%29%5C%2C%20dx%20" alt="LaTeX: \displaystyle \int\limits_{6}^{12} \left(5 x^{3} + 5 x^{2} - 6 x + 8\right)\, dx " data-equation-content=" \displaystyle \int\limits_{6}^{12} \left(5 x^{3} + 5 x^{2} - 6 x + 8\right)\, dx " /> . </p> </p><p> <p>The indefinite integtal is <img class="equation_image" title=" \displaystyle F(x)=\frac{5 x^{4}}{4} + \frac{5 x^{3}}{3} - 3 x^{2} + 8 x+C " src="/equation_images/%20%5Cdisplaystyle%20F%28x%29%3D%5Cfrac%7B5%20x%5E%7B4%7D%7D%7B4%7D%20%2B%20%5Cfrac%7B5%20x%5E%7B3%7D%7D%7B3%7D%20-%203%20x%5E%7B2%7D%20%2B%208%20x%2BC%20" alt="LaTeX: \displaystyle F(x)=\frac{5 x^{4}}{4} + \frac{5 x^{3}}{3} - 3 x^{2} + 8 x+C " data-equation-content=" \displaystyle F(x)=\frac{5 x^{4}}{4} + \frac{5 x^{3}}{3} - 3 x^{2} + 8 x+C " /> . Using the Fundamental Theorem of Calculus Part II gives <img class="equation_image" title=" \displaystyle F(12)-F(6)=\left(28464\right)-\left(1920\right) = 26544 " src="/equation_images/%20%5Cdisplaystyle%20F%2812%29-F%286%29%3D%5Cleft%2828464%5Cright%29-%5Cleft%281920%5Cright%29%20%3D%2026544%20" alt="LaTeX: \displaystyle F(12)-F(6)=\left(28464\right)-\left(1920\right) = 26544 " data-equation-content=" \displaystyle F(12)-F(6)=\left(28464\right)-\left(1920\right) = 26544 " /> . </p> </p>