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Questions: Algebra BusinessCalculus
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Integrate \(\displaystyle \int \sqrt{x^{2} - 81}\, dx\)
\(\displaystyle x=9 \sec{\left(\theta \right)} dx=9 \tan{\left(\theta \right)} \sec{\left(\theta \right)}\)\(\displaystyle \int 81 \tan^{2}{\left(\theta \right)} \sec{\left(\theta \right)}\, d\theta\)
\begin{question}Integrate $\int \sqrt{x^{2} - 81}\, dx$
\soln{9cm}{$x=9 \sec{\left(\theta \right)} dx=9 \tan{\left(\theta \right)} \sec{\left(\theta \right)}$$\int 81 \tan^{2}{\left(\theta \right)} \sec{\left(\theta \right)}\, d\theta$}
\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>Integrate <img class="equation_image" title=" \displaystyle \int \sqrt{x^{2} - 81}\, dx " src="/equation_images/%20%5Cdisplaystyle%20%5Cint%20%5Csqrt%7Bx%5E%7B2%7D%20-%2081%7D%5C%2C%20dx%20" alt="LaTeX: \displaystyle \int \sqrt{x^{2} - 81}\, dx " data-equation-content=" \displaystyle \int \sqrt{x^{2} - 81}\, dx " /> </p> </p><p> <p> <img class="equation_image" title=" \displaystyle x=9 \sec{\left(\theta \right)} dx=9 \tan{\left(\theta \right)} \sec{\left(\theta \right)} " src="/equation_images/%20%5Cdisplaystyle%20x%3D9%20%5Csec%7B%5Cleft%28%5Ctheta%20%5Cright%29%7D%20dx%3D9%20%5Ctan%7B%5Cleft%28%5Ctheta%20%5Cright%29%7D%20%5Csec%7B%5Cleft%28%5Ctheta%20%5Cright%29%7D%20" alt="LaTeX: \displaystyle x=9 \sec{\left(\theta \right)} dx=9 \tan{\left(\theta \right)} \sec{\left(\theta \right)} " data-equation-content=" \displaystyle x=9 \sec{\left(\theta \right)} dx=9 \tan{\left(\theta \right)} \sec{\left(\theta \right)} " /> <img class="equation_image" title=" \displaystyle \int 81 \tan^{2}{\left(\theta \right)} \sec{\left(\theta \right)}\, d\theta " src="/equation_images/%20%5Cdisplaystyle%20%5Cint%2081%20%5Ctan%5E%7B2%7D%7B%5Cleft%28%5Ctheta%20%5Cright%29%7D%20%5Csec%7B%5Cleft%28%5Ctheta%20%5Cright%29%7D%5C%2C%20d%5Ctheta%20" alt="LaTeX: \displaystyle \int 81 \tan^{2}{\left(\theta \right)} \sec{\left(\theta \right)}\, d\theta " data-equation-content=" \displaystyle \int 81 \tan^{2}{\left(\theta \right)} \sec{\left(\theta \right)}\, d\theta " /> </p> </p>