Application of Integrals

The fundamental approach involves dividing

The fundamental approach involves dividing the region under a curve into numerous thin vertical strips. Each strip has height y = f(x) and width dx, g

For a curve y = f(x)

For a curve y = f(x) bounded by x-axis and ordinates x = a and x = b, the area A = ∫[a to b] f(x) dx. This formula assumes the curve lies above the x-

When it's convenient to integrate

When it's convenient to integrate with respect to y, we use horizontal strips. For a curve x = g(y) bounded by y-axis and lines y = c and y = d, the a

When a curve lies below

When a curve lies below the x-axis, f(x) < 0, and the integral gives a negative value. For area calculations, we take the absolute value: |∫[a to b] f

To find the area between two

To find the area between two curves y = f(x) and y = g(x) where f(x) ≥ g(x) in the interval [a, b], we calculate A = ∫[a to b] [f(x) - g(x)] dx.