Analysis 3 (Integrals)

Subject 1: Indefinite Integral: The notion of primitive, constant of integration.

• Find the indefinite integral of:
• Level 1 : ע f(x)dx
• Level 2 : ע [f(x) + g(x)]dx
• Level 3 : ע 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) = -x² + 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) = ײ(3x-1)
• Level 5: Find F(x) given F(0) = 0.5 and F'(x) = ײSIN(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