Mathematical Methods · definite integrals · manipulative

Net area is the change in F

Shade f from a to b. On the antiderivative below, F(b) − F(a) is the vertical gap — the same number as the signed area.

f area f > 0 area f < 0 F

y = f(x) · integrand

y = F(x) · an antiderivative

Move a and b — the shaded net area and the gap F(b) − F(a) stay equal

Limits

−1
1.5
signed area
0
F(b) − F(a)
0

Working