Analysis 3 (Integrals)
Subject 1: Indefinite Integral: The notion of
primitive, constant of integration.
 Find the indefinite integral of:
 Level 1 : ò f(x)dx
 Level 2 : ò [f(x) + g(x)]dx
 Level 3 : ò 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) = Ö(3x1)
 Level 5: Find F(x) given F(0) = 0.5 and F'(x) = ÖSIN(x+2)
Subject 3: Calculation of area and volume of
revolution.
 Level 1 : The area bounded by the graph of f and
the xaxis
 Level 2 : The area bounded by the graphs of f and
g
 Level 3 : The volume of a solid of revolution
