Section 8.7 Improper Integrals I

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Presentation transcript:

Section 8.7 Improper Integrals I MAT 1235 Calculus II Section 8.7 Improper Integrals I http://myhome.spu.edu/lauw

HW WebAssign 8.7 Part I

Basic Idea

Probability & Statistics

Other Applications Laplace Transform to solve Differential Equations (MAT 3237) Physics (QM)

Preview Two types of Improper Integrals Infinite Intervals Discontinuous Integrands 𝑝-integrals (Use in section 8.7 Part II, Calculus III) Comparison Theorem

Preview Two types of Improper Integrals Infinite Intervals Discontinuous Integrands 𝑝-integrals (Use in section 8.7 Part II, Calculus III) Comparison Theorem

Fundamental Theorem of Calculus Part 1

Fundamental Theorem of Calculus Part 1

Type I

Improper Integral of Type I The integral is convergent if the limit exists. Otherwise, it is divergent.

Example 1

Remarks Must have the limit notations Can be divide into 2 steps

Example 2

Remarks

𝒑-integrals (Standard Result) Use in 8.7 Part II (Comparison Theorem) Calculus III

Example 3

Improper Integral of Type I

Example 4

Example 4

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