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. $$ \int_{0}^{2} \frac{1}{(x-1)^{4 / 3}} d x $$
Explain why the integral is improper and determine whether it diverges or converges. Evaluate the integral if it converses. $$ \int_{0}^{4} \frac{1}{\sqrt{x}} d x $$
Marginal Analysis In Exercises 27 and 28, use a program similar to the Simpson's Rule program on page 906 with \(n=4\) to approximate the change in revenue from the marginal revenue function \(d R / d x .\) In each case, assume that the number of units sold \(x\) increases from 14 to 16 . $$ \frac{d R}{d x}=50 \sqrt{x} \sqrt{20-x} $$
Use the error formulas to find bounds for the error in approximating the integral using (a) the Trapezoidal Rule and (b) Simpson's Rule. (Let \(n=4 .\).) $$ \int_{0}^{2} x^{3} d x $$
Use a program similar to the Simpson's Rule program on page 906 to approximate the integral. Use \(n=100\). $$ \int_{2}^{5} 10 x^{2} e^{-x} d x $$
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