Parametric integration

I’m doing the attached question.

I’m ok up until part c. I want it integrate the curve from point P to where the curve cuts the x axis which I think is when x =5 and if the integration is in trig then I shouldn’t be using that anyway. But what do I integrate. I suppose it’s 4 sin theta.

I looked at the answer and it integrates (4 sin theta)(-5 sin theta) between 0 and pi/4

I’m at a loss as to why any of that.

Thanks

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Reply 1

mqb2766

Original post by maggiehodgson

I’m doing the attached question.
I’m ok up until part c. I want it integrate the curve from point P to where the curve cuts the x axis which I think is when x =5 and if the integration is in trig then I shouldn’t be using that anyway. But what do I integrate. I suppose it’s 4 sin theta.
I looked at the answer and it integrates (4 sin theta)(-5 sin theta) between 0 and pi/4
I’m at a loss as to why any of that.
Thanks

Its doing parametric integration (chain rule) so
Int y dx = Int y dx/dt dt
https://www.savemyexams.com/a-level/maths_pure/edexcel/18/revision-notes/9-parametric-equations/9-2-further-parametric-equations/9-2-2-parametric-integration/

Really, putting in the dependencies youre doing
Int y(x) dx = Int y(x(t)) dx(t)/dt dt
So all you need to do is be clear about which representation/space youre working with.