C2 Quick Integration Question:

I've attached a diagram to hopefully make this a bit clearer.

Others have incorrectly said to integrate using 8 and 1 - you can only integrate between x-values.

So you need to find the x-values when y=8 and when y=1 and then integrate this. You should realise that you did this in part a). Now, if you look at my diagram you should see how you could split the graph into a rectangle and another area. Working out the area of the rectangle (which is in the shaded region) should be straightfoward, the vertical height is from 1 to 8.

However you must be careful, because when you integrated you calculated the area under the curve to the x-axis, and the shaded region does not include the x-axis. So you need to work out this area (straightforward) and take it away from the integrated area.

Area of rectangle + area of integrated area (with the bit at the bottom taken away) = total area

Ohhh, now it makes sense! Just one last question:

Ohhh, now it makes sense! Just one last question:

Not quite - remember in part a) you integrated from "2" to "1"? Those are the limits of the area you are finding. So you only found the area from x=2 to x=1

Ah thank you, it all makes sense now! Positive rating given for such a brilliant explanation!

Was this not obvious from post 9,10 and 13? You only needed to see why the shape at the bottom of your area was a rectangle.