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Q21 of 271 Page 307

Find the integrals of the functions.

sin^-1(cosx)

Let cosx = t

Then, sinx =

=> (-sinx)dx = dt

=> dx =

=> dx =

⇒ Now,

⇒

Let sin^-1 t = v

=>

⇒

⇒

⇒

…(1)

We know that,

sin-1x + cos-1 x =

⇒ sin^-1(cosx)=

Now, substituting in eq(1), we get,

⇒

⇒

⇒

⇒

⇒

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