In this unit students will cover the following IBSL Analysis and Approaches Standards:
SL 5.5
Introduction to integration as anti-differentiation for polynomial functions
Anti-differentiation with a boundary condition to determine the constant term
Definite integrals using technology
Area of a region enclosed by a curve y = f(x) and the x -axis, where f(x) > 0.
SL 5.9
Kinematic problems involving displacement s, velocity v, acceleration a and total distance traveled.
SL 5.10
Indefinite integral of x n (n ∈ ℚ), sinx, cosx, 1 x and ex
The composites of any of these with the linear function ax + b.
Integration by inspection (reverse chain rule) or by substitution for expressions of the form: ∫ kg′(x)f(g(x))dx.
SL 5.11
Definite integrals, including analytical approach.
Areas of a region enclosed by a curve y = f(x) and the x-axis, where f(x) can be positive or negative, without the use of technology. Areas between curves.
-IB Diploma Program Mathematics: Analysis & Approaches Guide