Turn on thread page Beta
 You are Here: Home >< Maths

# Does this work and if so how? watch

1. Ok, so i'm wondering if this will work and if so how? Can 4 be used for both parts because when we put it into sin we are assuming it is 4 radians and when we put it into the second part we are assuming it is 4 as an integer. Does this work?
2. (Original post by CIEBioloysifh)
Ok, so i'm wondering if this will work and if so how? Can 4 be used for both parts because when we put it into sin we are assuming it is 4 radians and when we put it into the second part we are assuming it is 4 as an integer. Does this work?
That's correct. You can use www.wolframalpha.com to check work like this by the way.

http://www.wolframalpha.com/input/?i...+1+and+x+%3D+4
3. (Original post by Mr M)
That;s correct. You can use www.wolframalpha.com to check work like this by the way.
I know it's correct, however, I came to TSR looking for a clear answer as to how this is the case as I'm really struggling to explain it to my friend. It's not the integration, it's the fact that plugging the value into the integral we use 4 as 4 radians and 4 as an integer in the second part.
4. (Original post by CIEBioloysifh)
I know it's correct, however, I came to TSR looking for a clear answer as to how this is the case as I'm really struggling to explain it to my friend. It's not the integration, it's the fact that plugging the value into the integral we use 4 as 4 radians and 4 as an integer in the second part.
If that's bugging you for some reason (and I don't really understand why it should) then treat this as two separate integrals. You'll get the same answer.

5. (Original post by Mr M)
If that's bugging you for some reason (and I don't really understand why it should) then treat this as two separate integrals. You'll get the same answer.

He's telling me that in the first section we are plugging in 4 radians and in the second section we're plugging in the integer 4, therefore the numbers we are plugging in aren't the same and they aren't the same limit for both terms because we are plugging in x= 4 radians
6. (Original post by CIEBioloysifh)
He's telling me that in the first section we are plugging in 4 radians and in the second section we're plugging in the integer 4, therefore the numbers we are plugging in aren't the same and they aren't the same limit for both terms because we are plugging in x= 4 radians
The radian measure of an angle is given by the ratio of two lengths so is unitless, since the metre units in the top and bottom cancel. A radian is therefore a "pure" number, and 4 radians is thus simply the integer 4, it's not 4 metres or 4 seconds or 4 "radian units", or whatever. You only know that 4 means 4 radians from the context in which it is used.

Does that explain it?
7. (Original post by CIEBioloysifh)
He's telling me that in the first section we are plugging in 4 radians and in the second section we're plugging in the integer 4, therefore the numbers we are plugging in aren't the same and they aren't the same limit for both terms because we are plugging in x= 4 radians
Radians are dimensionless so there really isn't a problem here. Just tell your friend to accept it. If he doesn't, he is certainly going to struggle to accept integration by substitution involving a trigonometric substitution!

Edit: atruser's explanation is better than mine.
8. (Original post by atsruser)
The radian measure of an angle is given by the ratio of two lengths so is unitless, since the metre units in the top and bottom cancel. A radian is therefore a "pure" number, and 4 radians is thus simply the integer 4, it's not 4 metres or 4 seconds or 4 "radian units", or whatever. You only know that 4 means 4 radians from the context in which it is used.

Does that explain it?
Yes thank you, that made it very clear to me, however, no luck with my friend still refusing to accept that the limit of the integral can be used this way.
9. (Original post by CIEBioloysifh)
Yes thank you, that made it very clear to me, however, no luck with my friend still refusing to accept that the limit of the integral can be used this way.
Does your friend also believe the Earth is flat? Mathematicians have been integrating happily for 350 years!
10. (Original post by CIEBioloysifh)
Yes thank you, that made it very clear to me, however, no luck with my friend still refusing to accept that the limit of the integral can be used this way.
It's not clear to me what he doesn't like, but here's another argument:

Consider two sin functions, one of which takes a radian argument (i.e. the usual calculus type of sin function) and one of which takes a degree argument. These are different functions because their domains differ e.g. we could have:

We can make the second out of the first by function composition. Let then and

Now we can write the integral

It should now be clear(?) that:

a) this integral makes sense, since we can write it all in terms of if we want.
b) the limit 4 is neither a radian nor a degree, since when we feed it to the first sin function, it works as a radian, and when we feed it to the second, it works as a degree.

[edit: of course, I got this wrong, since we actually feed the 4 into the integrated sin functions, namely the corresponding cos functions, but the point still stands]

Reply
Submit reply
Turn on thread page Beta
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: January 13, 2017
Today on TSR

### Cambridge interviews

Find out who is getting invitations

### University open days

• Heriot-Watt University
School of Textiles and Design Undergraduate
Fri, 16 Nov '18
• University of Roehampton
All departments Undergraduate
Sat, 17 Nov '18
• Edge Hill University
Faculty of Health and Social Care Undergraduate
Sat, 17 Nov '18
Poll
Useful resources

## Make your revision easier

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

Can you help? Study help unanswered threads

## Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.