MAT 1221 Survey of Calculus Section 6.2 The Substitution Rule

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Presentation transcript:

MAT 1221 Survey of Calculus Section 6.2 The Substitution Rule

Today The rest of the quarter 6.2 Return exam 2 to you Please take advantage of all the bonus points available to you!

What Does This picture Have To Do with Today’s Topic?

Preview Antiderivatives are difficult to find. We need techniques to help us. The substitution rule transforms a complicated integral into a easier integral. It is considered as the reverse process of the chain rule

The Smart Design of the Integral Notation The differential encoded the information of the independent variable. Placed at the right hand side to facilitate computations such as substitutions and integration by parts.

The Substitution Rule for Indefinite Integrals

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

Bottom Line… There are not too many choices.

Example 3

Example 4

Expectations Follow the hints Change your variables in one single step If you are done early, do your HW. I will wait for most of you to finish before returning the exam to you.