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Evaluate: int(-pi/2)^(2pi)sin^(-1)(sinx)...

Evaluate: `int_(-pi/2)^(2pi)sin^(-1)(sinx)dx`

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Verified by Experts

The graph of `f(x)=sin^(-1)(sin x)` is shown as in the following figure.

`=ubrace(-(1/2xx(pi)/2xx(pi)/2))_("for"-(pi)/2ltxlt0) +ubrace((1/2xxpixx(pi)/2))_("for"0ltxltpi)+ubrace((1/2xxpixx(pi)/2))_("for"piltxlt2pi)`
`=-(pi^(2))/8`
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CENGAGE-DEFINITE INTEGRATION -JEE Advanced Previous Year
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