Chapter 11: Problem 31
Use the Trapezoidal Rule with \(n=4\) to approximate the definite integral. $$ \int_{-1}^{1} \frac{1}{x^{2}+1} d x $$
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
The revenue from a manufacturing process (in millions of dollars per year) is projected to follow the model \(R=100\) for 10 years. Over the same period of time, the cost (in millions of dollars per year) is projected to follow the model \(C=60+0.2 t^{2}\), where \(t\) is the time (in years). Approximate the profit over the 10 -year period.
The integrand of the definite integral is a difference of two functions. Sketch the graph of each function and shade the region whose area is represented by the integral. $$ \int_{0}^{4}\left[(x+1)-\frac{1}{2} x\right] d x $$
The integrand of the definite integral is a difference of two functions. Sketch the graph of each function and shade the region whose area is represented by the integral. $$ \int_{-4}^{0}\left[(x-6)-\left(x^{2}+5 x-6\right)\right] d x $$
Lorenz Curve Economists use Lorenz curves to illustrate the distribution of income in a country. Letting \(x\) represent the percent of families in a country and \(y\) the percent of total income, the model \(y=x\) would represent a country in which each family had the same income. The Lorenz curve, \(y=f(x)\), represents the actual income distribution. The area between these two models, for
State whether the function is even, odd, or neither. $$ g(t)=2 t^{5}-3 t^{2} $$
What do you think about this solution?
We value your feedback to improve our textbook solutions.
