Trigo Integration

Integration exploitation clear identities or a trig substitution
Some integrals involving trigonometric functions can be evaluated by u blurtg the trigonometric identities. These allow the integrand to be written in an resource variate which may be to a greater extent am modify to integration. On occasions a trigonometric substitution will enable an integral to be evaluated. Both of these topics atomic number 18 described in this unit. In order to master the techniques explained here it is vital that you accept plenty of practice exercises so that they become second nature. after(prenominal) reading this text, and/or viewing the video tutorial on this topic, you should be able to: part trigonometric identities to meld misdeed2 x, cosine2 x, and functions of the form sin 3x cos 4x. integrate products of sines and cosines using a concoction of trigonometric identities and integration by substitution hire trigonometric substitutions to evaluate integrals

Contents
1. Introduction 2. Integrals requiring the use of trigonometric identities 3. Integrals involving products of sines and cosines 4. Integrals which make use of a trigonometric substitution 2 2 3 5

1

c mathcentre August 28, 2004

1.



Introduction
By now you should be come up aware of the important results that cos kx dx = 1 sin kx + c k 1 sin kx dx = ? cos kx + c k

However, a little more care is needed when we wish to integrate more complicated trigonometric functions such as sin2 x dx, sin 3x cos 2x dx, and so on. In case like these trigonometric identities can be used to write the integrand in an alternative form which can be integrated more readily. Sometimes, use of a trigonometric substitution enables an integral to be found. Such substitutions are described in Section 4.

2. Integrals requiring the use of trigonometric identities
The trigonometric identities we shall use in this section, or which are required to complete the Exercises, are summarised here: 2 sin A cos B 2 cos A cos B 2 sin A sin B 2 sin A + cos2 A cos 2A = = = = = = =...If you want to get a full essay, order it on our website: Orderessay



If you want to get a full essay, wisit our page: write my essay .