My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
December 2nd, 2012, 03:27 PM   #1
Member
 
Joined: Apr 2012

Posts: 72
Thanks: 3

solution of integral

cot(cos^-1 x)
mathLover is offline  
 
December 2nd, 2012, 06:36 PM   #2
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,168
Thanks: 472

Math Focus: Calculus/ODEs
Re: solution of integral

Rewrite the integrand using the identity:

then use the substitution:

to get:

MarkFL is offline  
December 2nd, 2012, 09:38 PM   #3
Member
 
Joined: Apr 2012

Posts: 72
Thanks: 3

Re: solution of integral

Thanks.
mathLover is offline  
December 2nd, 2012, 10:38 PM   #4
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,168
Thanks: 472

Math Focus: Calculus/ODEs
Re: solution of integral

Use the power-rule for integration:

where

along with the anti-derivative form of the fundamental theorem of calculus:

where .
MarkFL is offline  
December 3rd, 2012, 12:33 AM   #5
Member
 
Joined: Apr 2012

Posts: 72
Thanks: 3

Re: solution of integral

Can someone please post the way from start to the end?
mathLover is offline  
December 3rd, 2012, 12:40 AM   #6
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,168
Thanks: 472

Math Focus: Calculus/ODEs
Re: solution of integral

You cannot evaluate the resulting definite integral using the rules I posted?
MarkFL is offline  
December 3rd, 2012, 12:51 AM   #7
Member
 
Joined: Apr 2012

Posts: 72
Thanks: 3

Re: solution of integral

I tried, but I have an error somewhere. I got a division by zero.
mathLover is offline  
December 3rd, 2012, 01:05 AM   #8
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,168
Thanks: 472

Math Focus: Calculus/ODEs
Re: solution of integral

MarkFL is offline  
December 3rd, 2012, 01:23 AM   #9
Member
 
Joined: Apr 2012

Posts: 72
Thanks: 3

Re: solution of integral

How did you do this first step?
mathLover is offline  
December 3rd, 2012, 01:29 AM   #10
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,168
Thanks: 472

Math Focus: Calculus/ODEs
Re: solution of integral

is an angle in a right triangle where the ratio of the side adjacent to that angle and the hypotenuse is , so we may say that the adjacent side is and the hypotenuse is 1. By the Pythagorean theorem, we may then say the side opposite the angle is .

Since the cotangent function by definition is the ratio of the adjacent to the opposite, we then have:



When I was first learning this, I would draw a right triangle so that I could clearly see what I needed to find.
MarkFL is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
integral, solution



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
solve Integral for closed form solution neera84 Complex Analysis 4 July 1st, 2013 10:08 AM
What is the final solution and the way to solve the integral mathLover Calculus 5 May 20th, 2013 09:08 PM
Integral - compare solution debad Calculus 9 July 1st, 2012 02:18 AM
Integral, problem and solution missing working RiAt Calculus 8 April 13th, 2012 04:55 AM
solve Integral for closed form solution neera84 Calculus 2 December 31st, 1969 04:00 PM





Copyright © 2018 My Math Forum. All rights reserved.