• The concept of anti-derivative as the reverse of differentiation

• How to calculate the anti-derivative of polynomials and special functions

• How to calculate definite integrals and their relation to areas under graphs

• Applications of integration to calculating areas and solving problems in kinematics.

Week 1: Anti-differentiation

• Understand the concept of anti-derivative as the “reverse” of differentiation
• Calculate the anti-derivative of polynomials and special functions (including trigonometric and exponential functions).

Week 2: Definite integrals

• Understand the concept of definite integration as the (signed) area under the graph of a function and recognise it as the limit of Riemann sums
• Apply definite integration to solve a variety of problems relating to the area between curves.

Week 3: The fundamental theorem of calculus

Understand and apply the fundamental theorem of calculus to calculate definite integrals.

Week 4: Applications of integration

Apply integration to solve problems relating to areas between prescribed curves, basic motion/mechanics and initial value problems.

Week 5: Assessment

There is a timed exam.