My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum

LinkBack Thread Tools Display Modes
March 2nd, 2016, 06:18 PM   #1
Joined: May 2015
From: Earth

Posts: 64
Thanks: 0

Exclamation Confusion over the Fundamental Theorem

So I've been looking at ways to rewrite arcsin, and I found this:

arcsin (x/a) + C = the integral of 1 over the square root of a^2 minus x^2 dx

This is correct

But when I try to graph the DERIVATIVE of arcsin (x/a), I expected it to be the same graph as 1 over the square root of a^2 minus x^2 dx, which is the same thing as above but without the integral. However, this does not work, instead the a^2 must be a 1 for them to be the same. Why is this?
eglaud is offline  
March 2nd, 2016, 06:39 PM   #2
Math Team
Joined: Dec 2013
From: Colombia

Posts: 7,342
Thanks: 2465

Math Focus: Mainly analysis and algebra
Are you graphing it correctly, or is your derivative incorrect?

${\mathrm d \over \mathrm d x}\arcsin {x \over a} = \frac1a {1 \over \sqrt{1- \left({x \over a}\right)^2}}$
v8archie is offline  
March 2nd, 2016, 06:45 PM   #3
Math Team
Joined: Jul 2011
From: Texas

Posts: 2,761
Thanks: 1416

What value did you use for the constant, $a$? I used $a=3$, and graphed both the derivative of $\arcsin(x/3)$ and $\dfrac{1}{\sqrt{9-x^2}}$.

Note that I added 1 to the square root function, effectively shifting it up one unit so it could be seen ... without doing so, the two graphs were superimposed.
Attached Images
File Type: jpg image.jpg (12.0 KB, 1 views)

Last edited by skipjack; March 3rd, 2016 at 01:01 AM.
skeeter is online now  
March 2nd, 2016, 08:48 PM   #4
Joined: May 2015
From: Earth

Posts: 64
Thanks: 0

I see what I've done wrong, sorry guys, thanks for always offering help though!!
eglaud is offline  

  My Math Forum > College Math Forum > Calculus

confusion, fundamental, theorem

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Fundamental Theorem Omnipotent Calculus 6 November 30th, 2014 06:16 AM
Fundamental Theorem Omnipotent Calculus 1 November 27th, 2014 01:11 PM
Fundamental theorem of calculus Mr Davis 97 Calculus 6 June 5th, 2014 02:29 PM
the fundamental theorem ray Algebra 6 April 22nd, 2012 03:50 AM
Mean Value Theorem and complete confusion. E.L.Kim Calculus 1 July 26th, 2009 01:42 PM

Copyright © 2018 My Math Forum. All rights reserved.