1.

Statement-1: int_(0)^(pi//2) x cot x dx=(pi)/(2)log2 Statement-2: int_(0)^(pi//2) log sin x dx=-(pi)/(2)log2

Answer»

Statement-1 is TRUE, Statement-2 is True,Statement-2 is a correct explanation for Statement-1.
Statement-1 is True, Statement-2 is not a correct explanation for Statement-1.
Statement-1 is True, Statement-2 is False.
Statement-1 is False, Statement-2 is True.

Solution :Clearly, statement-2 is true. (SEE an important RESULT on page 44.16)
Now, `underset(0)overset(pi//2)int X cot x dx=[x log sin x]_(0)^(x//2)-underset(0)overset(pi//2)int log sin x dx`
`rArr underset(0)overset(pi//2)int x cot x dx=0underset(x to 0)LIM x logsin x-(-(pi)/(2)log2)`[Using Statement-2]
`rArr underset(0)overset(pi//2)int x cot x dx=(pi)/(2)log 2`
So, statement-1 is true. Also,Statement-2 is a correct explanation for statement.


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