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Statement-1:int_(0)^(1)(cos x)/(1+x^(2))dxgt(pi)/(4)cos1 Statement-2: If f(x) and g(x) are continuous on [a,b], then int_(a)^(b) f(x) g(x)dx=f(c )int_(a)^(b)g(x) for some c in (a,b). |
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Answer» Statement-1 is TRUE, Statement-2 is True,Statement-2 is a correct EXPLANATION for Statement-1. Using statement-2, these exists `c in(0,1)` such that `underset(0)overset(1)int (COSX)/(1+x^(2))dx=cos c underset(0)overset(1)int (1)/(1+x^(2))dx=(PI)/(4)cos c` Clearly, `cos c gt cos 1` for all `c in (0,1)` `rArr (pi)/(4)cos c gt (pi)/(4)cops 1` `rArr underset(0)overset(1)int(cos x)/(1+x^(2))dx gt (pi)/(4)cos 1` So, statement-1 is true. Also, statement-2 is a correct explanation for statement-1. |
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