Calculus
Class 12

Area Under Curve

A=abf(x)dxA = \int_a^b |f(x)| dx
0123456−1−0.500.51
Area = ∫[a to b]|f(x)|dx

Adjust Variables

Amplitude
A =
0.53

Geometric interpretation of definite integral. Absolute value ensures area is always positive.

Real-World Applications

Surveying — Land area with irregular boundaries.

Medicine — Drug bioavailability from concentration-time curve.

Physics — Work done = area under force-displacement graph.

Economics — Total revenue from demand curve.

Engineering — Material volume from cross-sectional profiles.

Statistics — Probability = area under probability density function.

Hydrology — Water volume from flow rate curve.

Energy — Power consumption from power-time graph.

Manufacturing — Material usage from profile curves.

Finance — Total returns from rate-of-return curve.

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