MAT 1235 Calculus II 4.5 Part I The Substitution Rule

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Presentation transcript:

MAT 1235 Calculus II 4.5 Part I The Substitution Rule

Homework WebAssign HW 4.5 I There are 28 problems. Do it early. These problems ensure you to attain certain degree of proficiency in this topic.

Preview Antiderivatives are difficult to find. We need techniques to help us. The substitution rule transforms a complicated integral into a easier integral. The procedures for indefinite and definite integrals are similar but different. Part I: Indefinite Part II Definite

Introductory Story The wonderful design of windshield wipers

Introductory Story The wonderful design of the integral notation…

The Substitution Rule for Indefinite Integrals

Remarks

Wonderful Design of Notation…

Example 1

You can always check the answer by differentiation:

Substitution Method

Expectations

Example 2

Example 3

Example 4

Example 5