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201.

`int_a^b(logx)/x dx=1/2log(a b) log(b/a)`A. `log((log b)/(log a))`B. `log (ab).log((b)/(a))`C. `(1)/(2).log(ab).log((b)/(a))`D. `(1)/(2).log(ab).log((a)/(b))`

Answer» Correct Answer - C
Discussion
202.

`int_(-10)^(10)log((a+x)/(a-x))dx=`A. `-2log(a+10)`B. `2log((a+10)/(a-10))`C. 0D. 20 log a

Answer» Correct Answer - C
Discussion
203.

`int_(0)^(pi//4)sqrt((1-sin2x)/(1+sin 2x))dx=`A. log 2B. `(1)/(2)log2`C. 2 log 2D. 4 log 2

Answer» Correct Answer - B
Discussion
204.

The value of `int _(0)^(pi//2) log ("cosec "x) dx` isA. `(pi)/(2)log 2`B. `pi log 2`C. `-(pi)/(2)log 2`D. `2pi log 2`

Answer» Correct Answer - A
Discussion
205.

The value of `int(8 log(1+x))/(1+x^(2)) dx` isA. `(pi)/(8).log2`B. `(pi)/(2).log 2`C. log 2D. `pi. log 2`

Answer» Correct Answer - D
Discussion
206.

`(x.sin^(-1)x^(2))/(sqrt(1-x^(4)))`A. `(6-pi sqrt(3))/(12)`B. `(4-3sqrt(3).pi)/(12)`C. `6-(pi)/(6)`D. none of these

Answer» Correct Answer - A
Discussion
207.

Show that `("lim")_(nvecoo)(1/(n+1)+1/(n+2)++1/(6n))=log6`A. log 2B. log 3C. log 6D. 0

Answer» Correct Answer - C
Discussion