# Integration

AS level

• Know and use the Fundamental Theorem of Calculus
• Integrate xn (excluding n = -1), and related sums, differences and constant multiples
• Evaluate definite integrals; use a definite integral to find the area under a curve

A level

• Integrate ekx, 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