Application of Integrals — Class 12 Mathematics

This chapter uses the definite integral to compute areas of plane regions. The area bounded by a curve , the -axis and the lines and is ; similarly, area with respect to the -axis uses . The area between two curves and over is . Standard applications include the area of regions bounded by circles, parabolas, ellipses and straight lines. Care is taken with the sign of the integrand — areas below the axis contribute positively in absolute value — and with finding the correct limits from the points of intersection of the curves. These techniques translate the abstract integral into concrete geometric measurement.