# Differentiation and Integration – Further Maths Paper 1

Candidates should be able to:

• obtain an expression for $$\dfrac{d^2y}{dx^2}$$ in cases where the relation between $$y$$ and $$x$$ is defined implicitly or parametrically;
• derive and use reduction formulae for the evaluation of definite integrals in simple cases;
• use integration to find:
• mean values and centroids of two- and three-dimensional figures (where equations are expressed in cartesian coordinates, including the use of a parameter), using strips, discs or shells as appropriate,
• arc lengths (for curves with equations in cartesian coordinates, including the use of a parameter, or in polar coordinates),
• surface areas of revolution about one of the axes (for curves with equations in cartesian coordinates, including the use of a parameter, but not for curves with equations in polar coordinates).