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# Section 5 - Ms. Monaco's Math ... Section 5.4 Exponential Functions – Differentiation and Integration The inverse of the natural log function is 𝑥= 𝑥-3 -2 -1 1 2 3-3-2-1 1

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### Text of Section 5 - Ms. Monaco's Math ... Section 5.4 Exponential Functions – Differentiation and...

• Section 5.4

Exponential Functions – Differentiation and Integration

• The inverse of the natural log function is 𝑓 𝑥 = 𝑒𝑥

-3 -2 -1 1 2 3

-3

-2

-1

1

2

x

y

• Ex1: Solve 17 xe 

• Ex2: Find the relative extrema of ( ) xf x xe

• Ex3: Integrate

a) b)3 1xe dx 2

5 xxe dx

• c) d)

1

2

xe dx

x cos(sin )( )xx e dx

• Ex4a: 1

0

xe dx

1

1

x

y

• Ex4b: 1

0 1

x

x

e dx

e

1

1

x

y

• Ex4c: 0

1

cos( )x xe e dx 

  

-1

1

x

y

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