AP Calculus BC – Chapter 6 Differential Equations and Mathematical Modeling 6.1: Antiderivatives and Slope Fields. Learning Objectives: Students will/I can… Construct antiderivatives using the Fundamental Theorem of Calculus.
Learning Objectives: Students will/I can…
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.
dy/dx = sec2 x + 2x + 5.
y(1) = 0.
1. Find the particular solution to the equation dy/dx = 2x – sec2x whose graph passes through the point (0, 3).
2. Find the solution to the differential equation f’(x)= e-x2 for which f(7) = 3.
3. Graph the family of functions that solves the differential equation
dy/dx = cos x.