Learning Materials
Features
Discover
Chapter 4: Problem 75
Horizontal Tangent Find a function \(f\) such that the graph of \(f\) has a horizontal tangent at \((2,0)\) and \(f^{\prime \prime}(x)=2 x\)
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
Using Symmetry Use the symmetry of the graphs of the sine and cosine functions as an aid in evaluating each definite integral. $$ \begin{array}{ll}{\text { (a) } \int_{-\pi / 4}^{\pi / 4} \sin x d x} & {\text { (b) } \int_{-\pi / 4}^{\pi / 4} \cos x d x} \\ {\text { (c) } \int_{-\pi / 2}^{\pi / 2} \cos x d x} & {\text { (d) } \int_{-\pi / 2}^{\pi / 2} \sin x \cos x d x}\end{array} $$
Even and Odd Functions In Exercises \(69-72,\) evaluate the integral using the properties of even and odd functions as an aid. $$ \int_{-2}^{2} x\left(x^{2}+1\right)^{3} d x $$
Show that the function \(f(x)=\int_{0}^{1 / x} \frac{1}{t^{2}+1} d t+\int_{0}^{x} \frac{1}{t^{2}+1} d t\) is constant for \(x>0\).
Approximation of \(\mathrm{Pi}\) In Exercises 43 and \(44,\) use Simpson's Rule with \(n=6\) to approximate \(\pi\) using the given equation. (In Section \(5.7,\) you will be able to evaluate the integral using inverse trigonometric functions.) $$ \pi=\int_{0}^{1 / 2} \frac{6}{\sqrt{1-x^{2}}} d x $$
Using Simpson's Rule Use Simpson's Rule with \(n=10\) and a computer algebra system to approximate \(t\) in the integral equation $$\int_{0}^{t} \sin \sqrt{x} d x=2$$
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