Download AP Calculus BC – 3.6 Chain Rule 1

AP Calculus BC – Chapter 6
Differential Equations and Mathematical Modeling
6.1: Antiderivatives and Slope Fields - Day 2
Goals: Construct antiderivatives using the Fundamental
Theorem of Calculus.
Find antiderivatives of polynomials, ekx, and selected
trigonometric functions of kx, as well as linear
combinations of these functions.
Solve initial value problems of the form dy/dx = f(X),
y0 = f(x0).
Construct slope fields using technology and interpret slope
fields as visualizations of differential equations.
Slope Field (direction field):
A slope field for the first-order differential
equation dy/dx = f(x, y) is a plot of
short line segments with slopes f(x, y)
for a lattice of points (x, y) in the plane.
Indefinite Integral:
The family of all antiderivatives of a
function f(x) is the indefinite integral
of f with respect to x and is denoted by
∫f(x)dx. IF F is any function such that
F’(x) = f(X), then ∫f(x)dx = F(x) + C,
where C is an arbitrary constant, called
the constant of integration.
Assignments:

CW: Activity.
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HW 6.1B: #3-51 (every 3rd), 52, 61.