You are Here: Home >< Maths

# Area under a curve question watch

1. The curve has the equation y=x^2+1 and the line has equation y=7-x. The finite region, R1, is bounded by the line and the curve. The finite region, R2, is below the curve and the line and is bounded by the positive x and y axes.

a) Find R1
b) Find R2

What I did is different to the solution given. I found R1 and R2 intersect at (-3,10) and (2,5). I used the limits 2 and -3 to find the area under the curve. Then to find the total area, I saw you could form a trapezium. I found the area of the trapezium and subtracted it from the area under the curve to find R1. Can someone tell me why that is wrong please?

The other way I just found out is to just subtract the area under y=7-x and y=x^2+1. This gets you the correct answer however I'm still not sure why my method 1st time was wrong?
2. (Original post by dont know it)
The curve has the equation y=x^2+1 and the line has equation y=7-x. The finite region, R1, is bounded by the line and the curve. The finite region, R2, is below the curve and the line and is bounded by the positive x and y axes.

a) Find R1
b) Find R2

What I did is different to the solution given. I found R1 and R2 intersect at (-3,10) and (2,5). I used the limits 2 and -3 to find the area under the curve. Then to find the total area, I saw you could form a trapezium. I found the area of the trapezium and subtracted it from the area under the curve to find R1. Can someone tell me why that is wrong please?

The other way I just found out is to just subtract the area under y=7-x and y=x^2+1. This gets you the correct answer however I'm still not sure why my method 1st time was wrong?
Although I am terrible at shapes and geometry, I am struggling to see the trapezium.

3. (Original post by dont know it)
The curve has the equation y=x^2+1 and the line has equation y=7-x. The finite region, R1, is bounded by the line and the curve. The finite region, R2, is below the curve and the line and is bounded by the positive x and y axes.

a) Find R1
b) Find R2

What I did is different to the solution given. I found R1 and R2 intersect at (-3,10) and (2,5). I used the limits 2 and -3 to find the area under the curve. Then to find the total area, I saw you could form a trapezium. I found the area of the trapezium and subtracted it from the area under the curve to find R1. Can someone tell me why that is wrong please?

The other way I just found out is to just subtract the area under y=7-x and y=x^2+1. This gets you the correct answer however I'm still not sure why my method 1st time was wrong?
Area under curve = 50/3

Area of trapezium = 1/2 (10+5)*5 = 75/2

Area in between = 75/2 - 50/3 = 125/6 which is correct.

You need to show us your calculation for us to determine what went wrong.
4. You may have tripped up in the areas or integration or some sort of calculator mistake.
5. (Original post by Kevin De Bruyne)
Although I am terrible at shapes and geometry, I am struggling to see the trapezium.

Not sure if my sarcasm detector is broken, but:

6. (Original post by dont know it)
The other way I just found out is to just subtract the area under y=7-x
Note that the area underneath a straight line between the points and is precisely a trapezium:

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: February 25, 2018
Today on TSR

### Results day under a month away

How are you feeling?

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams