Integration question? (1 Viewer)

[tlv6554]

Im so confused. When finding the area under a curve, and say the area falls both below and above the x-axis, do you let the two areas cancel each other out. My teacher says to take the absolute value and so just add them together but I found a question from the 1999 paper where the answers say to subtract the negative area from the sum of the two positive areas. Some clarification on this would be much appreciated ))

 

[frog1944]

If it asks you to find the area you must take the absolute value of the area if it is negative.

However, if it asks you to evaluate an integral (such as in the above question) which is not the same as asking for the area, you must sum the "areas" (inclusive of negative ones) i.e. you just add them together (leaving negative areas negative).

 

[pikachu975]

Im so confused. When finding the area under a curve, and say the area falls both below and above the x-axis, do you let the two areas cancel each other out. My teacher says to take the absolute value and so just add them together but I found a question from the 1999 paper where the answers say to subtract the negative area from the sum of the two positive areas. Some clarification on this would be much appreciated ))

Taking the absolute value of the negative area is the same as minusing it. This is why:

Say the positive area is P and the negative area is N

|N| + P = Area
But also P - N = Area because minusing a negative (- and -) gives it a positive, which is the same as doing absolute value.

 

[tlv6554]

Thank you everybody!