Trigonometric Integrals

Trigonometric Integrals

http://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/trigintdir...

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INTEGRATION OF TRIGONOMETRIC INTEGRALS

Recall the definitions definitions of the t he trigonometric trigonometric functions funct ions..

The following indefinite integrals involve all of these well-known trigonometric functions. Some of the following trigonometry identities may be needed. A.) B.) C.)

so that

D.)

so that

E.) F.)

so that

G.)

so that

It is assumed that you are familiar with the following rules of differentiation.

These lead directly to the following indefinite integrals.

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1.) 2.) 3.) 4.) 5.) 6.)

The next four indefinite integrals result from trig identities and u-substitution. 7.) 8.) 9.) 10.)

We will assume knowledge of the following well-known, basic indefinite integral formulas : , where

is a constant

, where

is a constant

Most of the following problems are average. A few are challenging. Many use the method of u-substitution. Make careful and precise use of the differential notation and and be careful when arithmetically and algebraically simplifying expressions.

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PROBLEM 1 :

Integrate

.

Click HERE to see a detailed solution to problem 1.

PROBLEM 2 :

Integrate

.


PROBLEM 3 :

Integrate

.


PROBLEM 4 :

Integrate

.


PROBLEM 5 :

Integrate

.


PROBLEM 6 :

Integrate

.


PROBLEM 7 :

Integrate

.


PROBLEM 8 :

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Integrate

.

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PROBLEM 9 :

Integrate

.


PROBLEM 10 :

Integrate

.


PROBLEM 11 :

Integrate

.


PROBLEM 12 :

Integrate

.


PROBLEM 13 :

Integrate


PROBLEM 14 :

Integrate

.


PROBLEM 15 :

Integrate

.


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PROBLEM 16 :

Integrate

.


PROBLEM 17 :

Integrate

.


PROBLEM 18 :

Integrate

.


PROBLEM 19 :

Integrate

.


Some of the following problems require the method of integration by parts. That is, .

PROBLEM 20 :

Integrate

.


PROBLEM 21 :

Integrate

.


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PROBLEM 22 :

Integrate

.


PROBLEM 23 :

Integrate

.


PROBLEM 24 :

Integrate

.


PROBLEM 25 :

Integrate

.


PROBLEM 26 :

Integrate

.


PROBLEM 27 :

Integrate

.


Click HERE to return to the original list of various types of calculus problems. Your comments and suggestions are welcome. Please e-mail any correspondence to Duane Kouba by clicking on the following address : [email protected]

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About this document ... Duane Kouba 2000-04-18

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Trigonometric Integrals

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