Analysis 3 — Integrals
Subject 1: Indefinite Integral: The notion of primitive, constant of integration.
- Find the indefinite integral of:
- Level 1 : ? f(x)dx
- Level 2 : ? [f(x) + g(x)]dx
- Level 3 : ? f(ax + b)dx
Subject 2: Finding a function by its derivative and one of its values.
- Level 1: Find F(x) given G(x) = SIN(x) - 1/x, F'(x) = G'(x) and G(2) = -1
- Level 2: Find F(x) given F(2) = -1 and F'(x) = -x 2 + 3x
- Level 3: Find F(x) given F(0) = 2 and F'(x) = COS(x)
- Level 4: Find F(x) given F(1) = 3 and F'(x) = ? (3x-1)
- Level 5: Find F(x) given F(0) = 0.5 and F'(x) = ? SIN(x+2)
Subject 3: Calculation of area and volume of revolution.
- Level 1 : The area bounded by the graph of f and the x-axis
- Level 2 : The area bounded by the graphs of f and g
- Level 3 : The volume of a solid of revolution