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 freeUse a program similar to the Simpson's Rule program on page 906 with \(n=6\) to approximate the indicated normal probability. The standard normal probability density function is \(f(x)=(1 / \sqrt{2 \pi}) e^{-x^{2} / 2}\). If \(x\) is chosen at random from a population with this density, then the probability that \(x\) lies in the interval \([a, b]\) is \(P(a \leq x \leq b)=\int_{a}^{b} f(x) d x\). $$ P(0 \leq x \leq 1.5) $$
Consumer Trends The rate of change \(S\) in the number of subscribers to a newly introduced magazine is modeled by \(d S / d t=1000 t^{2} e^{-t}, 0 \leq t \leq 6\), where \(t\) is the time in years. Use Simpson's Rule with \(n=12\) to estimate the total increase in the number of subscribers during the first 6 years.
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. $$ \int_{0}^{\infty} \frac{5}{e^{2 x}} d x $$
Approximate the integral using (a) the Trapezoidal Rule and (b) Simpson's Rule for the indicated value of \(n\). (Round your answers to three significant digits.) $$ \int_{0}^{1} \sqrt{1-x^{2}} d x, n=4 $$
Use a program similar to the Simpson's Rule program on page 906 with \(n=6\) to approximate the indicated normal probability. The standard normal probability density function is \(f(x)=(1 / \sqrt{2 \pi}) e^{-x^{2} / 2}\). If \(x\) is chosen at random from a population with this density, then the probability that \(x\) lies in the interval \([a, b]\) is \(P(a \leq x \leq b)=\int_{a}^{b} f(x) d x\). $$ P(0 \leq x \leq 1) $$
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