Find the area of the region bounded by the curve y = x², the x-axis and the lines x = 1 and x = 3.

1. 1 · Write what is given and what is to be found. Curve y = x², the x-axis and the lines x = 1 and x = 3. To find: the area of the region they enclose.
2. 2 · Draw the figure. Draw the parabola y = x² opening upwards from O. Draw x = 1 and x = 3, shade the region above the x-axis and draw one vertical strip of width dx.
3. 3 · Write the formula, rule or theorem. A = ∫ y dx from 1 to 3
4. 4 · Integrate.
   • A = ∫ x² dx from 1 to 3
   • = [x³/3] from 1 to 3
   • = 27/3 − 1/3 = 26/3
5. 5 · Check and box the answer. The region is above the x-axis, so the value is positive. Area = 26/3 sq units.

Scoring tip: Draw and shade the region first. A neat figure with a strip earns a mark in most marking schemes.