ACARA ACMMM132, Calculate the area under a curve

Calculate the exact area between a curve and the x-axis over an interval by evaluating the definite integral.

For a curve that stays above the x-axis, the area between it and the axis from a to b is exactly the definite integral. Sketch the region first, then evaluate F(b) - F(a). Give the area in square units.

Generated and checked in code, so it is correct.

Assuming the definite integral always equals the area, it only does so where the curve is above the axis; below the axis the integral is negative (a signed area), which is why this introduction keeps the curve positive.