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# SQA Higher Maths Basics of integration

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.

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.

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.

# 1

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.

# 3

Solve the integral ∫4x + 32x⁷dx.

# 4

Define indefinite integrals.

# 5

Evaluate ∫10x + 8dx.

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