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  • If [.] represent the greatest integers function , then the value of definte integral [[x^2]-cosx] under limit 0 to square root (pi/2)

If [.] represent the greatest integers function , then the value of definte integral [[x^2]-cosx] under limit 0 to square root (pi/2)

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Solution: We have ,

I=int_o^sqrtpi /2([x^2]+[-cosx])dx\ \Rightarrow 0< x< sqrtpi /2Rightarrow 0< x^2< pi /2\\Rightarrow I=int_0^1(0+[-cosx])dx +int_1^sqrtpi /2(1+[-cosx])dx=-1

Hence left | I ight |=1

 

 

Posted by

Deependra Verma

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