- #1
Maddie1609
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Homework Statement
Homework Equations
Doesn't the integral of sec x tan x equal sec x?
Maddie1609 said:Homework Statement
View attachment 89882
Homework Equations
Doesn't the integral of sec x tan x equal sec x?
The Attempt at a Solution
View attachment 89880
Great, thanks :-) Isn't the integral of sec x tan x equal to sec x?Ray Vickson said:Your textbook is correct. The attachment of your work is too small and blurry for me to read, so I will not even try. I will look at it if you type it out.
Yes, but I don't see how this fact applies to your question.Maddie1609 said:Great, thanks :-) Isn't the integral of sec x tan x equal to sec x?
Maddie1609 said:Great, thanks :-) Isn't the integral of sec x tan x equal to sec x?
Maddie1609 said:Isn't the integral of sec x tan x equal to sec x?
Thank you! I just went over it again and realized I forgot about the chain rule.Daeho Ro said:Well, it is correct, but the textbook uses the fact that [itex]\frac{d\tan x}{dx} = \sec^2 x[/itex]. If you use [itex] \frac{d(\sec x \tan x)}{dx} = \sec x [/itex], then the first part of integration will be
[tex] \int \sec^2 x \tan^2 x dx = \int \sec x \tan^2 x d(\sec x \tan x), [/tex]
which is not that easy to calculate. However, when you use [itex]\frac{d\tan x}{dx} = \sec^2 x[/itex], then
[tex] \int \sec^2 x \tan^2 x dx = \int \tan^2 x d(\tan x) = \dfrac{1}{3} \tan^3 x + C_1. [/tex]
I just realized as much myself I forgot about the chain rule, so I intgrated (sec x tan x)2 to be (sec3 x)/3.Mark44 said:Yes, but I don't see how this fact applies to your question.
Yes, it is not uncommon for textbooks to have errors. Textbooks are created by human beings who are prone to making mistakes. Additionally, textbooks go through many revisions and edits before being published, so errors can still slip through the cracks.
One way to find errors in your textbook is to carefully read and review the content. Look for inconsistencies, incorrect information, or typos. You can also cross-reference the information with other reliable sources to check for accuracy.
If you find an error in your textbook, you should first verify that it is indeed an error by cross-checking with other sources. Then, you can bring the error to the attention of the publisher or author. They may have a process in place for reporting errors and making corrections.
Yes, errors in textbooks can have serious consequences, especially in subjects like science and mathematics where accuracy is crucial. Students may misunderstand important concepts or equations if there are errors in the textbook, leading to incorrect learning and potential mistakes on exams or in real-world applications.
To prevent errors in textbooks, publishers and authors should have thorough review processes in place to catch mistakes before the book is published. Additionally, using reliable sources and fact-checking information can help to ensure accuracy in the content. However, it is important to remember that human error can still occur, so it is always a good idea to double-check information with multiple sources.