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SQA Higher Maths Basics of integration

Basics of integration

This page covers the following topics:

1. Integrating polynomials
2. Constant of integration
3. Indefinite integrals

The integral of a polynomial ax^n is given by ax^(n + 1)/(n + 1) + c, where c is the constant of integration.

Integrating polynomials

During differentiation, the constant terms of the function being differentiated will disappear. Thus, to account for this in integration, a constant is added to the integral. This constant is usually expressed as c and is called the constant of integration.

Constant of integration

Indefinite integrals do not have an evaluated constant of integration. They represent a family of functions which have the same derivative, and their only difference is the value of the constant of integration.

Indefinite integrals

1

A gradient function is given in the graph. Find the general form of the equations whose derivative follows the given gradient function.

A gradient function is given in the graph. Find the general form of the equations whose derivative follows the given gradient function.

2

Evaluate ∫10x + 8dx.

Evaluate ∫10x + 8dx.

3

Solve the integral ∫4x + 32x⁷dx.

Solve the integral ∫4x + 32x⁷dx.

4

Define indefinite integrals.

Define indefinite integrals.

5

Evaluate ∫10x + 8dx.

Evaluate ∫10x + 8dx.

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