Mathematical Methods · anti-differentiation · manipulative

Initial condition picks one antiderivative

f′ is known. The curves F + C form a vertical family — scrub C until the live curve passes through (a, b).

f′(x) F + C siblings live F + C (a, b)

y = f′(x) · known

y = F(x) + C · antiderivative family

Scrub C until the live curve hits the marked point · drag (a, b) to change the initial condition

Given f′

Constant C

0

Initial condition (a, b)

1
3

Drag the hot point on the family plot, or scrub a and b here.

Show

Antiderivative F + C
live curve for the current C
Sibling family
faint F + C curves nearby

Working