Antiderivatives (Integral) - Basic Trigonometric Integration Formulas, Slides of Differential and Integral Calculus

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ANTIDERIVATIVES

(INTEGRAL)

THE BASIC TRIGONOMETRIC

INTEGRATION FORMULAS

OBJECTIVES:

• recall and apply the different

trigonometric identities in simplifying a

function; and

• integrate trigonometric functions using

their differentials as the basis for

evaluation

RIGONOMETRIC IDENTITIES:

Reciprocal Identities:

tan u

6 .cot u csc u

3 .tan u cos cu

5 .sec u sec u

2 .cos u sin u

4 .csc u csc u

1 .sin u  

Pythagorean Identities:

3 .cot u 1 ccs u

2. 1 tan u sec u

1 .sin u cos u 1

2 2 2 2 2 2

RIGONOMETRIC IDENTITIES:

Double Angle Identities:

1 tan u 2 tan u 3 .tan 2 u 1 2 sin u 2 cos u- 1 2 .cos 2 u cos u- sin u 1 .sin 2 u 2 sinu cosu 2 2 2 2 2 

Half-Angle

Identities:

   1 cos 2 u

2. sin u

1 cos 2 u

1. cos u

2 2

  dx sin 2 x 1 5

2 tan 2 x    dx 1 cot 3 x 3 2 cos 3 x

2 3         dx 2 x cot 2 x

3. tan 2

dx sin 2 x 4

log 25 sec 2 x      dx 1 cos 2 x x cot x 2 x

2 1 1    dx 1 sin 2 x sin 2 x 1

     dx 1 csc 3 / x 2 x

2 

8. cos 2 x 2 sin 2 x 1 dx 2 2   dx 1 tan e e log csc e

2 x x 2 x 

10. xe dx lnsec x^2

RCISES: Evaluate each of the following integr