| Statement-1: If [.] denotes the greatest integer function then the integral \[\int\limits_{0}^{\pi /2}{\frac{{{e}^{\sin x-[\sin x]}}d({{\sin }^{2}}x-[{{\sin }^{2}}x])}{\sin x-[\sin x]}}\] is equal to 0 |
| Statement-2: \[fog(x)\] is an odd function, if f and g both are odd functions |
A) Statement-1 and 2 are true and Statement-2 is correct explanation of Statement-1.
B) Statement-1 and 2 are true and Statement-2 is not correct explanation of Statement-1.
C) Statement-1 is true, statement-2 is false
D) Statement-1 is false, Statement-2 is true.
Correct Answer: B
Solution :
\[\int\limits_{0}^{\pi /2}{\frac{{{e}^{\{\sin x\}}}d\{{{\sin }^{2}}x\}}{\{\sin x\}},}\]where {.} denotes the fractional part of x. \[=\int\limits_{0}^{\pi /2}{\frac{{{e}^{\sin x}}d({{\sin }^{2}}x)}{\sin x}}\] \[0<x<\pi /2,\Rightarrow 0<\sin x<1\]and {sinx}=sinx \[=\int\limits_{0}^{1}{\frac{{{e}^{\sqrt{t}}}dt}{\sqrt{t}}}=2.\]
You need to login to perform this action.
You will be redirected in
3 sec
