# Integration Help

Watch
#1

How on earth would you know that the area between π/4 and 3π/4 = -1? I tried integrating, taking into account that a and b are constants, so you end up with something like (sin(3π/4)) - (sin(π/4)) = √2/2 - √2/2 = 0? I am really confused. Anyway, the total value is supposed to come out as -½.
0
3 years ago
#2
(Original post by pickerco)
How on earth would you know that the area between π/4 and 3π/4 = -1?.
You are supposed to see this by using the symmetry of cosine. If the are above the line from 0 to pi/4 is 1/2, then it should be easy to see that the area below the line is twice this, that is, 1, because the interval from pi/4 to 3pi/4 is twice the interval from 0 to pi/4. But if you integrate from pi/4 to 3pi/4, you'll get -1 because it is below the line. All you now have to do is add these integrals together.

It's only two marks because you are exxpected to use these symmetry ideas rather than do any integration.
1
3 years ago
#3
(Original post by pickerco)

How on earth would you know that the area between π/4 and 3π/4 = -1? I tried integrating, taking into account that a and b are constants, so you end up with something like (sin(3π/4)) - (sin(π/4)) = √2/2 - √2/2 = 0? I am really confused. Anyway, the total value is supposed to come out as -½.
First you need to see that the area under the curve between 0 and pi/4 is half the area above the curve between pi/4 and 3pi/4. Can you see why that must be true? Notice that acos(bx) is a vertical/horizontal stretch of the cos(x) graph - the cos(x) graph has not been translated at all.

You don't need to do any actual integration to do this question. It's all about understanding the relationship between integrals and area.
1
#4
That makes absolutely perfect sense, thank you so much guys

I have literally woken up, had breakfast and been focusing on maths the whole day and really need to take a break. I think I'm going to start frying my brain lol. I've got my final exams very soon and it's really important I get A in maths and chemistry, I'm just really determined to do well, so I've been studying a lot these last few days. But thanks, I did get a bit confused with the acosbx because I realised it actually hasn't even done anything to the graph relative to where it is on the y axis i.e. it's not even been moved up or down but I kept thinking that, I just got confused but I get it now. Thanks again
1
3 years ago
#5
(Original post by pickerco)
That makes absolutely perfect sense, thank you so much guys

I have literally woken up, had breakfast and been focusing on maths the whole day and really need to take a break. I think I'm going to start frying my brain lol. I've got my final exams very soon and it's really important I get A in maths and chemistry, I'm just really determined to do well, so I've been studying a lot these last few days. But thanks, I did get a bit confused with the acosbx because I realised it actually hasn't even done anything to the graph relative to where it is on the y axis i.e. it's not even been moved up or down but I kept thinking that, I just got confused but I get it now. Thanks again
Please keep asking maths questions in this forum if you have any.

And good luck for the rest of your revision
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.

### Poll

Join the discussion

#### Current uni students - are you thinking of dropping out of university?

Yes, I'm seriously considering dropping out (103)
13.27%
I'm not sure (33)
4.25%
No, I'm going to stick it out for now (239)
30.8%
I have already dropped out (19)
2.45%
I'm not a current university student (382)
49.23%