“Teach A Level Maths” Vol. 1: AS Core Modules 25: Definite Integration © Christine Crisp

Module C1 Module C2 AQA Edexcel MEI/OCR OCR "Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages"

The numbers on the integral sign are called the limits of integration is a definite integral The numbers on the integral sign are called the limits of integration

Evaluating the Definite Integral The definite integration results in a value. e.g.1 Find the indefinite integral but omit C

Evaluating the Definite Integral The definite integration results in a value. e.g.1 Draw square brackets and hang the limits on the end

Evaluating the Definite Integral The definite integration results in a value. e.g.1 Replace x with the top limit the bottom limit

Evaluating the Definite Integral The definite integration results in a value. e.g.1 Subtract and evaluate

Evaluating the Definite Integral The definite integration results in a value. e.g.1 So,

SUMMARY The method for evaluating the definite integral is: Find the indefinite integral but omit C Draw square brackets and hang the limits on the end Replace x with the top limit the bottom limit Subtract and evaluate

Evaluating the Definite Integral e.g. 2 Find Solution: Indefinite integral but no C

Evaluating the Definite Integral e.g. 2 Find Solution: Substitute for x: top limit minus bottom limit Simplify

Evaluating the Definite Integral In this example, if we can’t use a calculator, we can save time by collecting terms from both brackets. We must be very careful with the signs

Exercises 1. Find 2. Find

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Evaluating the Definite Integral The definite integration results in a value. So, e.g.1

SUMMARY Find the indefinite integral but omit C Draw square brackets and hang the limits on the end Replace x with the top limit the bottom limit Subtract and evaluate The method for evaluating the definite integral is: