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Another Integration Question

Hi, sorry to bother you all again, I have another question. I'm just trying to make sure I understand everything because unfortunately I can't use TSR in the real exam.

I was told that integration finds the area between a curve and the axis. If this is true, does this mean that in this example: if I integrated x2+2 x^2 + 2 between the limits of -2 & 2, I would get the area in yellow and the area below the curve until the line y=0 y = 0

This cannot be true as I found the area beneath y=6 y = 6 with the same limits and I got 24.

So, what area did I actually find when I integrated?

https://gyazo.com/010e62bc1c73abf65e5182fe3eb67a80
If you integrated between -2 and 2, you just found the area below the curve bounded by the lines x=-2, x=2, and y=0. In other words, the "area below the curve until the line y=0", but not the area in yellow.
Reply 2
Avatar for Naruke
Naruke
OP
11
Original post by constellarknight
If you integrated between -2 and 2, you just found the area below the curve bounded by the lines x=-2, x=2, and y=0. In other words, the "area below the curve until the line y=0", but not the area in yellow.



but I was told
Original post by 16Characters....
Integration finds the area between the curve and the axis.
Reply 3
Avatar for Naruke
Naruke
OP
11
Original post by constellarknight
If you integrated between -2 and 2, you just found the area below the curve bounded by the lines x=-2, x=2, and y=0. In other words, the "area below the curve until the line y=0", but not the area in yellow.


So to be 100% certain, when integrating a curve between limits, I will only find the area under the curve between those limits? yes?
Reply 4
Avatar for Naruke
Naruke
OP
11
=(
Reply 5
Avatar for B_9710
B_9710
18
Integration always finds the area under the curve (or more specifically the area between the curve and the axis of the variable you're integrating with respect to. When integrating with respect to x between 2 x limits you integrate as shown in the diagram.
image.jpg

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