`int_(0)^(1)cos^(-1)xdx` का मान ज्ञात कीजिए ।

Answer

1

Explanation

माना `x=cost`
`rArr" "dx=-sint dt`
`{:(x=0," पर ",cost=0,rArr.,t=pi//2),(x=1," पर ",cost=1,rArr., t=0):}`
`therefore int_(0)^(1)cos^(-1)x dx = - int_(pi//2)^(0)t sin t dt`
`" "=-[{-t cost}_(0)^(pi//2)-int_(pi//2)^(0)1.(-cost)dt]`
`" "=+((pi)/(2)cos.(pi)/(2)-0)-[sint]_(pi//2)^(0)`
`" "=0-(sin0-sin.(pi)/(2))=1`