Chapter 12: Problem 30
Use partial fractions to find the indefinite integral. $$ \int \frac{x^{4}}{(x-1)^{3}} d x $$
Chapter 12: Problem 30
Use partial fractions to find the indefinite integral. $$ \int \frac{x^{4}}{(x-1)^{3}} d x $$
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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. $$ \int_{0}^{9} \frac{1}{\sqrt{9-x}} d x $$
Revenue The revenue (in dollars per year) for a new product is modeled by \(R=10,000\left[1-\frac{1}{\left(1+0.1 t^{2}\right)^{1 / 2}}\right]\) where \(t\) is the time in years. Estimate the total revenue from sales of the product over its first 2 years on the market.
Use a program similar to the Simpson's Rule program on page 906 to approximate the integral. Use \(n=100\). $$ \int_{1}^{4} x^{2} \sqrt{x+4} d x $$
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}^{2} x^{2} d x, n=4
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. $$ \int_{1}^{\infty} \frac{1}{x^{2}} d x $$
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