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A level maths Integration spec question?

Do we have to integrate ∫x dy, not really clear on the spec. Help would be great thanks
Reply 1
Original post by Fesdces1
Do we have to integrate ∫x dy, not really clear on the spec. Help would be great thanks

Your question isn't really clear. Is x supposed to be a function of y in that expression?

What you call the variable of integration isn't important - you could define u as a function of t and integrate u(t) dt, and so on! The "spec" shouldn't need to tell you that :smile:
Reply 2
Original post by davros
Your question isn't really clear. Is x supposed to be a function of y in that expression?
What you call the variable of integration isn't important - you could define u as a function of t and integrate u(t) dt, and so on! The "spec" shouldn't need to tell you that :smile:

Screenshot 2025-02-02 15.22.19.png An example of the type of thing im on about
Reply 3
Original post by davros
Your question isn't really clear. Is x supposed to be a function of y in that expression?
What you call the variable of integration isn't important - you could define u as a function of t and integrate u(t) dt, and so on! The "spec" shouldn't need to tell you that :smile:

Ive done every question in the textbook and not once have I had a question that you had to consider the region as it your looking from the y-axis instead of the x-axis (If that makes sense)
Reply 4
Original post by Fesdces1
Screenshot 2025-02-02 15.22.19.png An example of the type of thing im on about

Neglecting the parametric part, but you flip between
Int y(x) dx
and
Int x(y) dy
when you consider volumes of revolution about x or y axes for instance. It shouldnt be a big deal when you think of it simply as a riemann sum with either vertical or horizontal rectangles.
(edited 1 month ago)
Reply 5
Original post by mqb2766
Neglecting the parametric part, but you flip between
Int y(x) dx
and
Int x(y) dy
when you consider volumes of revolution about x or y axes for instance. It shouldnt be a big deal when you think of it simply as a riemann sum with either vertical or horizontal rectangles.

I feel like you are my maths tutor at this point, dedication from you is crazy. I dont think volumes of revolutions are apart of my specification (I think it got moved to FM)
Reply 6
Original post by Fesdces1
I feel like you are my maths tutor at this point, dedication from you is crazy. I dont think volumes of revolutions are apart of my specification (I think it got moved to FM)

Quite possibly for volumes of revolution, but its probably best to say its on the boundary of the spec, so you should be able to do it with a nudge, as its not really different from the usual integration set up as davros noted.
(edited 1 month ago)
Reply 7
Original post by mqb2766
Quite possibly for volumes of revolution, but its probably best to say its on the boundary of the spec, so you should be able to do it with a nudge, as its not really different from the usual integration set up as davros noted.

Okay so Ill just make sure Im familiar with the process, thank you
Reply 8
Original post by Fesdces1
Okay so Ill just make sure Im familiar with the process, thank you

At the end of the day, you simply swap the x and y axes and proceed as normal.
Reply 9
Original post by mqb2766
At the end of the day, you simply swap the x and y axes and proceed as normal.

Yeah I understand the question its not too bad, just wanted to know If it 100% isnt on the spec because then I wouldnt waist my time

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