Integration Q: Sums and Differences of Areas (1 Viewer)

[hc.pmt]

Hey guys,
can anyone help me with this question - its been doing my head in for a while.
Its question 13, Ex. 3.8. of Maths In Focus:

Find the area bounded by the curve y = x² + 2x - 8 and the line y = 2x + 1

Any help is appreciated - worked solutions even more so :]

 

[Drongoski]

 

[hc.pmt]

can someone please explain WHY i have to deduct the curve from the line?

 

[sazlik]

The area between the two curves is the difference between the areas of the two curves. (If you don't know which curve is above the other then you need to use the absolute value to obtain a positive area.)



This is true for all positions of the curves—so long as they don't cross each other between x=a and x=b.

Hope that helps?

 

[hscishard]

The area between the two curves is the difference between the areas of the two curves. (If you don't know which curve is above the other then you need to use the absolute value to obtain a positive area.)



This is true for all positions of the curves—so long as they don't cross each other between x=a and x=b.

Hope that helps?

I would sketch it. Then see which is above which. If I still can't find it, I'll just sub a value in both equations that is between the points of intersection. Then which ever is greater, must be on top[Therefore it is g(x) in Integral: g(x)-f(x)]

Is there a quicker way?

 

[sazlik]

I would sketch it. Then see which is above which. If I still can't find it, I'll just sub a value in both equations that is between the points of intersection. Then which ever is greater, must be on top[Therefore it is g(x) in Integral: g(x)-f(x)]

Is there a quicker way?

It doesn't matter which you subtract from the other, really—so long as you take the absolute value (because area can't be negative.) You get the same magnitude either way—only the sign differs. I'm almost 100% sure I'm right on this, but if I'm not please feel free to correct me otherwise.

 

[hscishard]

Nice. Did you make that up? Or was that from a textbook. If it was from the textbook gimme its name .

 

[sazlik]

Nope, I didn't make it up. Our teacher told us...but yep, it's in our textbook too. 3 Unit Mathematics Book 1, Jones & Couchman. (Published by Longman.)

 

[sazlik]

Oh, that is—I have the combination advanced/extension book, but the same chapter is also in the 2 Unit Book 1, I'm pretty sure.

 

[hscishard]

Very interesting. I'll browse through the library and hog that book.

 

[bouncing]

yup sazlik is 100% correct...

it makes no difference what order the curves are subtracted as long as there is an absolute value outside.. i think this method (of using absolutes) is incredibly fast when it comes to those annoying curves that cannot be drawn (or if you are one who has trouble identifying which is above the other)

pps i got 36 units as well