Quick integration between curves (1 Viewer)

[tommykins]

how to find the area between x² + 2x -8 and 2x+1 ?

I was away today and i missed out on the lesson. I can do all the questions in the text book but ahve no idea how to approach this one.

Thanks in advance.

 

[watatank]

draw the curves. the area between them is just the whole area of the top curve minus the area of the smaller curve right?

so your answer is

integral [ (2x+1) - (x² + 2x -8) ]

don't forget to consider limits and stuff but you should be sweet if you draw a picture.

 

[tommykins]

Thank you.

How about -6x + 16 and x^2 ? I tried the same thing but I got it wrong.

I once again did the same technique with x^3 and -3x+4, got it wrong though.

EDIT - I got it right the second time, but I am confused about how x^2 -(-6x+16) gives the right integral.

Oh and also, does this technique apply to all parabolas with parabolas? and hyperbola's with hyperbolas/parabolas? Or does it have to be with a straight line?

Should I just do it the normal way..splitting things up etc. ?

 

[RedZenith]

(int x^2 dx) - (int (-6x+16)dx) = int (x^2 + 6x - 16) dx is the correct integral.

Generally when you want to find the bounded area between two curves, you need to subtract the curve below from the curve on top. Therefore you need to find the intersections between the graphs and adjust your limits of integration according to them.