Learning Materials
Features
Discover
Chapter 11: Problem 30
Find the indefinite integral and check your result by differentiation. $$ \int\left(x^{3}-4 x+2\right) d x $$
Over 30 million students worldwide already upgrade their learning with 91影视!
All the tools & learning materials you need for study success - in one app.
Get started for free
Use a symbolic integration utility to evaluate the definite integral. \(r^{6}\). $$ \int_{2}^{5}\left(\frac{1}{x^{2}}-\frac{1}{x^{3}}\right) d x $$
Use the Midpoint Rule with \(n=4\) to approximate the area of the region bounded by the graph of \(f\) and the \(x\) -axis over the interval. Compare your result with the exact area. Sketch the region. $$ f(x)=x^{2}(3-x) \quad[0,3] $$
Use the Midpoint Rule with \(n=4\) to approximate the area of the region. Compare your result with the exact area obtained with a definite integral. $$ f(y)=4 y-y^{2}, \quad[0,4] $$
A company purchases a new machine for which the rate of depreciation can be modeled by \(\frac{d V}{d t}=10,000(t-6), \quad 0 \leq t \leq 5\) where \(V\) is the value of the machine after \(t\) years. Set up and evaluate the definite integral that yields the total loss of value of the machine over the first 3 years.
Sketch the region bounded by the graphs of the functions and find the area of the region. $$ y=\frac{1}{x^{2}}, y=0, x=1, x=5 $$
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine