Integration, definite integrals, areas and kinematics

Learning objectives

Understand integration as the reverse of differentiation, find indefinite integrals of polynomial terms axⁿ (n ≠ −1), and use a boundary condition to determine the constant of integration

Integrate xⁿ for rational n, sin x, cos x, 1/x and eˣ, together with composites of these with a linear function ax + b

Integrate by inspection (the reverse chain rule) or by a simple substitution for integrands of the form k g′(x) f(g(x))

Evaluate definite integrals analytically and with technology, and use them to find the area between a curve and the x-axis, including regions below the axis, and the area between two curves

Solve kinematics problems involving displacement, velocity and acceleration, using differentiation and integration to move between them and finding the total distance travelled