Chapter 12: Problem 26
Use partial fractions to find the indefinite integral. $$ \int \frac{x^{2}+12 x+12}{x^{3}-4 x} d x $$
Chapter 12: Problem 26
Use partial fractions to find the indefinite integral. $$ \int \frac{x^{2}+12 x+12}{x^{3}-4 x} d x $$
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Get started for freeDetermine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. $$ \int_{3} \frac{1}{x^{2} \sqrt{x^{2}-9}} d x $$
Use a program similar to the Simpson's Rule program on page 906 to approximate the integral. Use \(n=100\). $$ \int_{1}^{4} x \sqrt{x+4} d x $$
Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the indicated value of \(n\). Compare these results with the exact value of the definite integral. Round your answers to four decimal places. $$ \int_{0}^{1} \frac{1}{1+x} d x, n=4 $$
Use the error formulas to find \(n\) such that the error in the approximation of the definite integral is less than \(0.0001\) using (a) the Trapezoidal Rule and (b) Simpson's Rule. $$ \int_{1}^{3} \frac{1}{x} d x $$
Determine the amount of money required to set up a charitable endowment that pays the amount \(P\) each year indefinitely for the annual interest rate \(r\) compounded continuously. $$ P=\$ 12,000, r=6 \% $$
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