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Consider two functions `f (x) ={[x] , -2 leq x leq -1 and |x|+1 , -1 lt x leq 2 and g(x)={[x], -pi leq x lt 0 and sin x and 0 leq x leq pi`, where [.] denotes the greatest integer function.A. `(sqrt(3))/(4)+(pi)/(6)` sq. unitsB. `(sqrt(3))/(2)+(pi)/(6)` sq. unitsC. `(sqrt(3))/(4)-(pi)/(6)` sq. unitsD. `(sqrt(3))/(2)-(pi)/(6)` sq. units |
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Answer» Correct Answer - A `A=2overset(1//2)underset(0)intsqrt(1-x^(2))dx` `=2[(x)/(2)sqrt(1-x^(2)):|_(0)^((1)/(2))+(1)/(2) sin^(-1)x:|_(0)^((1)/(2))]` `= (sqrt(3))/(4)+(p)/(6)` sq. unit. |
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