I keep getting “Definite integral as area” questions wrong in Applications of Integrals. What's the trap?
treating area below the x-axis as positive.
The usual trap: treating area below the x-axis as positive. How to avoid it: area under the axis counts negative in a plain definite integral. Go back to the definition — the definite integral of f(x) between a and b gives the signed area between the curve and the x-axis.
Key point
Definite integral as area
Common mistake
treating area below the x-axis as positive.
Memory tip
area under the axis counts negative in a plain definite integral.
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