Geometrical Interpretation of Definite Integral


If we construct the graph of the integrand y = f(x), then for f(x) ≥ 0, the definite integral is numerically equal to the area bounded by the curve y = f(x), the x-axis and the straight lines x = a and x = b

 

In general represents an algebraic sum of the areas of the figures bounded by the graph of the function y = f(x), the x-axis and the straight lines x = a and x = b.

The areas above the x-axis enter into this sum with a plus sign, while those below the x-axis enter it with a minus sign (shown in figure).