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

Definite Integration Module C1 AQA Edexcel OCR MEI/OCR Module C2 "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"

Definite Integration The numbers on the integral sign are called the limits of integration e.g.1 is a definite integral

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

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

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

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

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

Definite Integration 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:

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

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

Definite Integration 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

Definite Integration Exercises 1. Find 2. Find

Definite Integration

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

Definite Integration 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: