Trap 1 - Signed vs Geometric Area: The integral from 0 to 2*pi of sin(x) dx = 0, but the area is 4. Always clarify whether the problem asks for the integral or the bounded area. "Area bounded by" always means the positive geometric area.

Trap 2 - Missing Intersection Points: Students find one pair of intersection points and miss another. Always solve the system completely. For y = $x^2$ and y = 4, x = +/-2, not just x = 2.

Trap 3 - Wrong Curve on Top: Assuming the first-mentioned curve is on top without checking. Always verify with a test point. Between y = sin(x) and y = cos(x), which is on top changes at every pi/4 + n*pi.

Trap 4 - Forgetting to Split: When curves cross within the interval, computing a single integral gives a value smaller than the actual area (due to cancellation). Example: area between y = $x^3$ and y = x from -1 to 1 requires splitting at x = -1, 0, 1.

Trap 5 - Wrong Variable: Using dx when dy is simpler (or vice versa). For x = $y^2$ and x = 2-$y^2$, dy gives one integral; dx requires three.

Trap 6 - Piecewise Functions: Forgetting that |f(x)| creates breakpoints. Always identify where the expression inside the absolute value changes sign.

Trap 7 - Parametric Direction: Not taking absolute value in parametric area formula. The integral can be negative depending on the direction of traversal.