Differentiating functions given parametrically
In this article we shall explore how to find the gradient of a curve that has been given in parametric form. The important rule to remember when working with curves that have been described...
Tagged: Calculus
Integration: Negative areas
This chapter explores negative areas. It covers understanding that areas below the x axis are negative, calculating areas under a curve, some or all of which may be under the x axis. Before attempting...
Implicit differentiation
This chapter explores implicit differentiation. The chapter covers differentiating a function defined implicitly; Finding equations of tangents and normals to curves defined implicitly. Before attempting this chapter you must have prior knowledge of basic...
Special Triangles and Identities
This chapter explores special triangles and identities. It covers identities and finding exact values of sine, cosine, and tangent of common angles. Before attempting this chapter you must have prior knowledge of basic trigonometry...
Integration by Parts – Twice
This chapter explores integration by parts twice. The chapter covers using the method of integration by parts twice to integrate much more complex functions, and using standard trigonometric integrals in integration by parts. Before...
Partial Fractions
This chapter explores partial fractions. The objectives for this chapter are to be able to express a fraction with linear fractions in the denominator as partial fractions and expressing a fraction with repeated linear...
Using Partial fractions
This chapter explores partial fractions. The objective for this chapter is to integrate a fraction using partial fractions. Before attempting the chapter you must have prior knowledge of partial fractions, and integrating simple fractions...
Integrating fractions
This chapter explores integrating fractions. It covers recognising integrals of the form; …and integrating fractions using the chain rule backwards. Before attempting this chapter you must have prior knowledge of integrating simple fractions by...
Solids of Revolution
When you take a fraction such as y = f(x) or between two limits on the x-axis and rotate this part of the curve around the x-axis the shape formed will be a 3...
Integration by substitution
One form of integration is the integration by inspection method which I have covered here. It might be best for your benefit to go through that revision before attempting this reading, it might make...