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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 |
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Answer» Statement-1 is TRUE, Statement-2 is True,Statement-2 is a correct explanation for Statement-1. 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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