ACARA ACMMM125, Definite integral as area under a curve
Year 11-12 · Mathematical Methods
Interpret the definite integral of f(x) from a to b as the area under the curve y=f(x) when f(x) is positive over the interval.
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Teaching guide
Interpret the definite integral of f(x) from a to b as the area under the curve y=f(x) when f(x) is positive over the interval.
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.
Math worksheets
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