Integration (1 Viewer)

[mac1996]

Hey guys
how would you do the question attached?

thank you

 

[Shadowdude]

Integration is just finding the area under the curve, pretty much.

So you just... add or subtract the areas using your Year 7 or 8 techniques.

Add the stuff above the x-axis. Subtract the stuff below the x-axis...

 

[Carrotsticks]

I presume the top limit is 4.

Break up the total area into many little pieces, and find the area of each individual piece.

If the piece is below the x axis, then it is considered 'negative area' and if it is above the x axis, it is considered 'positive area'.

So for example, from 0 to 1 in (a), we have pi/4 because it is a quarter of a circle of radius 1.

However, from 1 to 2 in (a), we have -1/2 because it's a half of a square with side length 1, but it is BELOW the x axis, so it is negative.

Repeat this process for each 'piece' and add them all up (don't worry if you get a negative answer, that is okay).

 

[mac1996]

thanks guys, i really appreciate your help