# C4 Integration - AreaWatch

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#1
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.
0
1 year ago
#2
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.
This is in TSR help.

I have asked for it to be moved to Maths
0
1 year ago
#3
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: = 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 !
0
#4
(Original post by Chittesh14)
I assume you mean the x-axis and not the z-axis.

You need to use the formula of the area of a curve: = 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   0
1 year ago
#5
Yeah I don't know why I wasn't thinking of that formula... Thank you though   No worries .
0
#6
(Original post by Chittesh14)
No worries .
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).
0
1 year ago
#7
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).
Nice one . Post some more questions if you find anything else difficult!
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