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(Higher SQA) maths - Finding the area between a curve and 2 lines ?

Not sure if I can explain this well without an image, but I am struggling to figure out how to find the area enclosed by a curve and TWO lines.

I can do every other question apart from these with no problem; normally just finding the integral of upper - lower bound to the limits found by using y1 = y2. But how do you do that with 3 functions (e.g a curve with 2 horizontal lines inside it enclosing an area if that makes sense)? I can't seem to get it no matter how hard I try! It's probably really easy and I'm overthinking it tbh. I will be asking my teacher for help, but I figured someone here might be able to help too.

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by kirstiin
Not sure if I can explain this well without an image, but I am struggling to figure out how to find the area enclosed by a curve and TWO lines.
I can do every other question apart from these with no problem; normally just finding the integral of upper - lower bound to the limits found by using y1 = y2. But how do you do that with 3 functions (e.g a curve with 2 horizontal lines inside it enclosing an area if that makes sense)? I can't seem to get it no matter how hard I try! It's probably really easy and I'm overthinking it tbh. I will be asking my teacher for help, but I figured someone here might be able to help too.

Probably a few ways and it would help to see the question, but if you wanted to integrate y = 1/x^2 between y=1 and y=2 (two horizontal lines), you could flip / invert the integration problem to
x = 1/sqrt(y)
and integrate that between 1 and 2 so
Int_1^2 1/sqrt(y) dy

0r you could integrate over x as normal and split the integration area up into a rectangle and an area under the curve. Or ...
(edited 1 year ago)

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