Learning Materials
Features
Discover
Chapter 11: Problem 36
Find the indefinite integral and check your result by differentiation. $$ \int \frac{1}{4 x^{2}} d x $$
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
Determine which value best approximates the area of the region bounded by the graphs of \(f\) and \(g\). (Make your selection on the basis of a sketch of the region and not by performing any calculations.) \(f(x)=2-\frac{1}{2} x, \quad g(x)=2-\sqrt{x}\) (a) 1 (b) 6 (c) \(-3\) (d) 3 (e) 4
Use the value \(\int_{0}^{1} x^{2} d x=\frac{1}{3}\) to evaluate each definite integral. Explain your reasoning. (a) \(\int_{-1}^{0} x^{2} d x\) (b) \(\int_{-1}^{1} x^{2} d x\) (c) \(\int_{0}^{1}-x^{2} d x\)
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 value \(\int_{0}^{2} x^{3} d x=4\) to evaluate each definite integral. Explain your reasoning. (a) \(\int_{-2}^{0} x^{3} d x\) (b) \(\int_{-2}^{2} x^{3} d x\) (c) \(\int_{0}^{2} 3 x^{3} d x\)
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. $$ \int_{0}^{4}\left[(x+1)-\frac{1}{2} x\right] d x $$
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