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Find the value of int(0)^(100pi)sin^(-1)...

Find the value of `int_(0)^(100pi)sin^(-1)(sin x)dx`.

Text Solution

Verified by Experts

`I=underset(0)overset(100opi)(int)sin^(-1)(sin x)dx`
In the graph of `y=sin^(-1)(sin x), x in [0, 100pip)`, there are 50 triangles above the x-axis and 50 tiangles below the x-axis.
`"Hence "=underset(0)overset(100opi)(int)sin^(-1)(sin x)dx=0`
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