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OCR A-level Maths Basics of integration

Basics of integration

This page covers the following topics:

1. Fundamental theorem of calculus
2. Integrating polynomials
3. Constant of integration
4. Indefinite integrals

The Fundamental Theorem of Calculus states that integration is the inverse process of differentiation. 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.

Fundamental theorem of calculus

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

Demonstrate the Fundamental Theorem of Calculus using the following equation: y = 10sinx + 6x + 10.

Demonstrate the Fundamental Theorem of Calculus using the following equation: y = 10sinx + 6x + 10.

3

The integral of a function is sinx + 20x. Find the derivative of the function.

The integral of a function is sinx + 20x. Find the derivative of the function.

4

Evaluate ∫10x + 8dx.

Evaluate ∫10x + 8dx.

5

Given that the integral of a function is 12xΒ³ + 21x + c, find the derivative of the function.

Given that the integral of a function is 12xΒ³ + 21x + c, find the derivative of the function.

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