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These are the statements describing what students need to learn:

- know and use the Fundamental Theorem of Calculus
- integrate x
^{n}(excluding n = -1) and related sums, differences and constant multiples.

Integrate e^{kx}, 1/x, sin kx , cos kx and related sums, differences and constant multiples - evaluate definite integrals; use a definite integral to find the area under a curve and the area between two curves
- Understand and use integration as the limit of a sum.
- carry out simple cases of integration by substitution and integration by parts; understand these methods as the inverse processes of the chain and product rules respectively (Integration by substitution includes finding a suitable substitution and is limited to cases where one substitution will lead to a function which can be integrated; integration by parts includes more than one application of the method but excludes reduction formulae)
- integrate using partial fractions that are linear in the denominator
- evaluate the analytical solution of simple first order differential equations with separable variables, including finding particular solutions (Separation of variables may require factorisation involving a common factor.)
- interpret the solution of a differential equation in the context of solving a problem, including identifying limitations of the solution; includes links to kinematics

Click on a statement above for suggested resources and activities from Transum.