More on Integration Formulas Lesson Slides: 15 Slides

15 Slides • 7 Questions

1

More on Integration Formulas

2

Objective

Solving Indefinite Integrals involving Logarithmic, Exponential and Trigonometric functions.

3

Introduction

4

5

Let us first recall the following differentiation formulas of Exponential and Logarithmic functions.

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Multiple Choice

Find the derivative of $f\left(x\right)\ =e^x$

1

$e^x$

2

e

3

x

4

$e^x+C$

7

Multiple Choice

Find the derivative of $f\left(x\right)=a^x$

1

$a^x$

2

$a^x\ln a$

3

$\ln a$

4

$a^x\ln a+C$

8

Multiple Choice

Find the derivative of $f\left(x\right)=\ln x$

1

$\frac{1}{x}+C$

2

$\ln x$

3

$\frac{1}{x}$

4

$\ln\left|x\right|+C$

9

Because antidifferentiation is the inverse operation of differentiation, the following formula should be immediate

10

Antidifferentiation Rules Involving Exponential and Logarithmic Functions

11

Multiple Choice

What is the $\int\ \frac{9}{x}dx?$

1

$9\ln\left|x\right|+C$

2

9x + C

3

9lnx

4

9ln + C

12

Multiple Choice

What is the $\int2e^xdx?$

1

$e^x+C$

2

$2e^x+C$

3

$2e^x$

4

$+C$

13

Multiple Choice

What is the $\int5^xdx?$

1

$\ln5+C$

2

$5x+C$

3

$\frac{5^x}{\ln5}+C$

4

$\frac{5^x}{\ln5}-C$

14

Multiple Choice

What is the $\int2^xdx?$

1

$\frac{2^x}{\ln2}+c$

2

$2^{x+C}$

3

$2^x+c$

15

Find the antiderivative

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General Rules For The Integral of Exponential and Logarithmic Functions

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Integrate the following

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Integration of Trigonometric Functions

Recall...

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Integration of Trigonometric Function

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Integrals of Trigonometric Functions

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More on Integration Formulas

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