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# C2 Integration Question: watch

1. What do I have to do for this question? :/

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2. (Original post by creativebuzz)
What do I have to do for this question? :/

I'm guessing you've done part A and you've got a problem with part B. So obviously, there's no one-step method to get the shaded area. However, if I tell you that you can get that area by subtracting the area under one line from the area under another, does that help?
3. (Original post by Chlorophile)
I'm guessing you've done part A and you've got a problem with part B. So obviously, there's no one-step method to get the shaded area. However, if I tell you that you can get that area by subtracting the area under one line from the area under another, does that help?

For part (a) I differentiated to get

dy/dx = 5 - 4x

I then subbed in the 1

to get a gradient of dy/dx = 1

then I did the negative reciprocal to get the normal gradient, which means my gradient is -1

I then subbed that into the line equation to get

y - 3 = -(x-1)

y-3=-x+1

x+y-4=0

Is that correct or have I gone wrong somewhere?

As for (b) I thought of doing the area of trapezium minus the area under the line and the curve! Is that correct or?
4. (Original post by creativebuzz)
For part (a) I differentiated to get

dy/dx = 5 - 4x

I then subbed in the 1

to get a gradient of dy/dx = 1

then I did the negative reciprocal to get the normal gradient, which means my gradient is -1

I then subbed that into the line equation to get

y - 3 = -(x-1)

y-3=-x+1

x+y-4=0

Is that correct or have I gone wrong somewhere?

As for (b) I thought of doing the area of trapezium minus the area under the line and the curve! Is that correct or?
For (a) that is correct, well done. For (b) yes that's basically right, the shaded area is the area under the line (i.e. a trapezium) minus the area under the curve. Make sure the limits are right though!
5. (Original post by Chlorophile)
For (a) that is correct, well done. For (b) yes that's basically right, the shaded area is the area under the line (i.e. a trapezium) minus the area under the curve. Make sure the limits are right though!
Awesome! I've found the area of the trapezium

As for the limits, I set the equation of the curve equal to zero and my result was x = 0 and x=5/2! Is that correct?
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