A-level Mathematics/Edexcel/Core 1/Integration
Basics of integration
Integration is the opposite of differentiation. For a power of x, you add 1 to the power, divide by the new power and add c, the constant of integration. Note that this rule will not work when the power of x is -1, this requires more advanced methods. The constant of integration is required because if a constant (i.e. a number without x in it) is differentiated it will become zero, and from just integration there is no way to determine the value of this constant.
Fractions with an x term in the denominator cannot be integrated as they are; the x term must be brought up to the working line. This can be done easily with the laws of indices.
Determining the value of c
You may be given a point on a curve and asked to determine the value of the constant of integration, c. This is quite simple, as the point is given as ; the values of x and y can be plugged in and the equation solved for c.
- The the gradient of the curve c is given by .
- The point lies on c. Hence, find the equation for c.
- Plug in values x = 3, y = 12.