1.

If intsqrt(2)(sqrt(1+sinx)dx=4cos(ax+b)+c, then the value of a,b are

Answer»

`(1)/(2),(pi)/(4)`
`1,(pi)/(2)`
1,1`
none of these

Solution :LET `l=intsqrt(2)SQRT(1+sinx)dx`
`=sqrt(2)int("sin"(x)/(2)+"COS"(x)/(2))dx`
`{because+-sqrt(1+sinA)=sin((A)/(2))+cos((A)/(2))]`
`=2intsin((pi)/(4)+(x)/(2))dx`
`=-4cos((x)/(2)+(pi)/(4))+C`
But `l=-4cos(ax+b)+c`
On comparing, we get
`a=(1)/(2),b=(pi)/(4)`.


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