91Ó°ÊÓ

Integration Technique Describe how to integrate a rational function with a numerator and denominator of the same degree.

Improper Integrals Describe two ways for an integral to be improper.

Guidelines for Solving the Basic Equation In your own words, explain how to solve a basic equation obtained in a partial fraction decomposition that involves quadratic factors.

Using Wallis's Formulas In Exercises 15-20, use Wallis's Formulas to evaluate the integral. $$\int_{0}^{\pi / 2} \cos ^{3} x d x$$

Special Integration Formulas In Exercises \(15-18\) , use the Special Integration Formulas (Theorem 8.2 ) to find the indefinite integral. $$\int \sqrt{9+4 x^{2}}$$

Using Wallis's Formulas In Exercises 15-20, use Wallis's Formulas to evaluate the integral. $$\int_{0}^{\pi / 2} \sin ^{9} x d x$$

Using Wallis's Formulas In Exercises 15-20, use Wallis's Formulas to evaluate the integral. $$\int_{0}^{\pi / 2} \cos ^{11} x d x$$

Evaluating a Definite Integral In Exercises \(43-52,\) evaluate the definite integral. Use a graphing utility to verify your result. $$\int_{0}^{3} x e^{x / 2} d x$$

Modeling Data The predicted cost \(C\) (in hundreds of thousands of dollars) for a company to remove \(p \%\) of a chemical from its waste water is shown in the table. $$\begin{array}{|c|c|c|c|c|c|}\hline P & {0} & {10} & {20} & {30} & {40} \\\ \hline C & {0} & {0.7} & {1.0} & {1.3} & {1.7} \\ \hline\end{array}$$ $$\begin{array}{|c|c|c|c|c|c|}\hline P & {50} & {60} & {70} & {80} & {90} \\\ \hline C & {2.0} & {2.7} & {3.6} & {5.5} & {11.2} \\ \hline\end{array}$$ A model for the data is given by $$C=\frac{124 p}{(10+p)(100-p)}$$ for \(0 \leq p<100 .\) Use the model to find the average cost of removing between 75\(\%\) and 80\(\%\) of the chemical.

Area In Exercises 63 and \(64,\) find the area of the region bounded by the graphs of the equations. $$y=\frac{x}{\sqrt{x+3}}, y=0, x=6$$