C4 Integration - Area

Need help with this problem:


A graph shows part of the curve C with parametric equations

x = (t+1)^2, y= 1/2 t^3 +3, t>=-1

P is the point on the curve where t=2. The line S is the normal to C at P.

a.) Find an equation of S

The shaded region R is bounded by C, S, the z-axis and the line with equation X=1.

b.) Using integration and showing all your working, find the area of R.

I've done part a. In part b I think I know what to do just not sure how to write out the integral. I don't know if I need to use the two parametric equations (and multiply or add them??) or use some other equation.

Need help with this problem:


A graph shows part of the curve C with parametric equations

x = (t+1)^2, y= 1/2 t^3 +3, t>=-1

P is the point on the curve where t=2. The line S is the normal to C at P.

a.) Find an equation of S

The shaded region R is bounded by C, S, the z-axis and the line with equation X=1.

b.) Using integration and showing all your working, find the area of R.

I've done part a. In part b I think I know what to do just not sure how to write out the integral. I don't know if I need to use the two parametric equations (and multiply or add them??) or use some other equation.

I assume you mean the x-axis and not the z-axis.

You need to use the formula of the area of a curve:
$\int^1_0 y\ dx$ = $\int^1_0 y\ (dx/dt) dt$

Parametric integration.

You will have to also work out the area under the normal. I haven't drawn the graph out so I can't visualise it, but it may involve subracting areas etc.

It'd be great if you can post a picture of the question and your working out !

Yeah I don't know why I wasn't thinking of that formula... Thank you though

No worries .
Have you done it? If you haven't, I'll help you tomorrow, sorry for the late reply.

Yeah, I did it. I got 58.9 as the area. By doing the integration with y and dx/dt ( = 2(t+1) ) and t limits 2 and 0. Then I added the previous value (34.4) to the area of the triangle (24.5).

Yeah I don't know why I wasn't thinking of that formula... Thank you though

what book is that. Dr frost said edexcel hadn't posted the exercise that question is from yet so how is it in a book XD