# A Level further maths- Integration using trig functionsWatch

Announcements
Thread starter 1 month ago
#1
Hi,

So I got this integral I can't seem to integrate:

Integral(limits 1.5 , 0.5) 1/(4x^2 -4x+5)
So I first completed the square (correctly)
Then I integrated it:
(Answer says there is a 0.5 here)[0.5arctan((2x-1)/2)] with limits 1.5 and 0.5
But this is somehow wrong because there is supposedly a factor of 0.5. Does anyone know where this extra 0.5 come from?

Thanks
0
1 month ago
#2
(Original post by Yodalam)
Hi,

So I got this integral I can't seem to integrate:

Integral(limits 1.5 , 0.5) 1/(4x^2 -4x+5)
So I first completed the square (correctly)
Then I integrated it:
(Answer says there is a 0.5 here)[0.5arctan((2x-1)/2)] with limits 1.5 and 0.5
But this is somehow wrong because there is supposedly a factor of 0.5. Does anyone know where this extra 0.5 come from?

Thanks
i think they made a mistake.... it should be 0.25 in front, not 0.5
0
Thread starter 1 month ago
#3
(Original post by the bear)
i think they made a mistake.... it should be 0.25 in front, not 0.5
The constant at the front is 0.25, I got 0.5. So there is an extra 0.5 and I am confused about where that extra number comes from
0
1 month ago
#4
(Original post by Yodalam)
The constant at the front is 0.25, I got 0.5. So there is an extra 0.5 and I am confused about where that extra number comes from
are you saying the book agrees with me ?

0
1 month ago
#5
(Original post by Yodalam)
Hi,

So I got this integral I can't seem to integrate:

Integral(limits 1.5 , 0.5) 1/(4x^2 -4x+5)
So I first completed the square (correctly)
Then I integrated it:
(Answer says there is a 0.5 here)[0.5arctan((2x-1)/2)] with limits 1.5 and 0.5
But this is somehow wrong because there is supposedly a factor of 0.5. Does anyone know where this extra 0.5 come from?

Thanks
It's because therefore we have

Now let then and we obtain

and obviously this evaluates to between the limits you got.
0
Thread starter 1 month ago
#6
(Original post by the bear)
are you saying the book agrees with me ?

Yes
0
1 month ago
#7
(Original post by Yodalam)
Yes

.... it should say (2x-1)/2 in the last line
Last edited by the bear; 1 month ago
1
Thread starter 1 month ago
#8
(Original post by RDKGames)
It's because therefore we have

Now let then and we obtain

and obviously this evaluates to between the limits you got.
Thanks,

So do I have to use substitution whenever there is a constant next to x in the integral? Because normally when there isnt an a constant next to x, substitiution is not needed. (I am talking about the (2x-1)^2 the 2 next to the x inside the bracket btw.
0
1 month ago
#9
(Original post by Yodalam)
Thanks,

So do I have to use substitution whenever there is a constant next to x in the integral? Because normally when there isnt an a constant next to x, substitiution is not needed. (I am talking about the (2x-1)^2 the 2 next to the x inside the bracket btw.
the standard result refers to the integral of 1/( x2 + a2 )
0
1 month ago
#10
(Original post by Yodalam)
Thanks,

So do I have to use substitution whenever there is a constant next to x in the integral? Because normally when there isnt an a constant next to x, substitiution is not needed. (I am talking about the (2x-1)^2 the 2 next to the x inside the bracket btw.
You should be aiming to use a substitution all the time whenever the integral isn't in its standard form. The very point of this is reduce it *to* a standard form from which you can just smack on the known results.
Last edited by RDKGames; 1 month ago
0
Thread starter 1 month ago
#11
Ok. thanks for your help!
0
1 month ago
#12
Np... is fun and practice. We used to attempt these in our heads when I was 20. No solution implies there is none... but you never know. You may come up with the warp field!
1
1 month ago
#13
Maxwell... Newton, all the greats came up with tricks no-one had previously considered. Maths is like magic... voila... a rabbit! WTF? Show me again!
0
X

new posts
Back
to top
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### University open days

• Norwich University of the Arts
Thu, 23 Jan '20
• SOAS University of London
Development Studies, Interdisciplinary Studies, Anthropology and Sociology, Languages, Cultures and Linguistics, Arts, Economics, Law, History, Religions and Philosophies, Politics and International Studies, Finance and Management, East Asian Languages & Cultures Postgraduate
Sat, 25 Jan '20
• University of Huddersfield
Sat, 25 Jan '20

### Poll

Join the discussion

#### How are your mock exams going?

Love them - Feeling positive (0)
0%
They've been reasonable (3)
50%
Not feeling great... (3)
50%
They are TERRIBLE! (0)
0%