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To Evaluate

Method : Let N = numerator = a cosx + b sinx

D = denominator = c cosx + d sinx

We find two constants l and m such that N = l (D) + m (D’) where D' =

i.e. a cos x + b sin x = ( l c + m d ) cos x + ( l d - m c ) sin x. Equating co-efficients of cos x and sin x, we get \ a = (c + md) and b= (d - mc). By solving these equations, simultaneously, we obtain l and m. Putting these values in (1) we can write the given integral as :


Example 44

Evaluate

Solution : We find constants l and m such that N = lD + mD’ ........(1)

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Index

6.1 Anti-derivatives (indefinite Integral)
6.2 Integration Of Some Trignometric Functions
6.3 Methods Of Integration
6.4 Substitution And Change Of Variables
6.5 Some Standard Substitutions
6.6 Integration By Parts
6.7 Integration By Partial Fractions

Chapter 7





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