What is the integral of cos(sin^-1x).EXPLAIN WITH VALID REASONS

Asked by GeoffreyRichards | 5th Nov, 2010, 07:48: PM

Expert Answer:

Dear Student,

∫cos(sin-1x)dx……………………….(1)

Let x = siny……………………………(2)

dx = cosy dy

Substitute it in integral (1)

=>∫cos(sin-1siny).cosy dy

=>∫cos(y).cosy dy

=>∫cos2y dy

=>∫(1+cos2y)/2 dy

=> ½ ∫dy + ½ ∫cos2y dy

=> y/2 +sin2y/4 +Constant

Substituting the value of y from equation (2) as y = sin-1x

(sin-1x)/2 + [sin{2(sin-1x)}]/4

Regards Topperlearning.

Answered by  | 6th Nov, 2010, 12:48: PM

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