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Engineering Mathematics
book

Engineering Mathematics

by Babu Ram
June 2009
Intermediate to advanced content levelIntermediate to advanced
1100 pages
42h 22m
English
Pearson India
Content preview from Engineering Mathematics
14.7 EVALUATION OF REAL DEFINITE INTEGRALS

We shall now discuss the application of Cauchy's Residue theorem to evaluate real definite integrals.

(A) Integration around the unit circle

We consider the integrals of the type

 

image

 

where the integrand is a rational function of sin θ and cos θ. Substitutet z = e. Then, dz = i e = iz dθ and

 

image

 

Thus (47) converts inZto the integral

 

image

 

where φ(z) is a rational function of z and C is the unit circle ...

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Publisher Resources

ISBN: 9789332515611