The imaginary part of `(1+i)` a) `e^((pi)/(2))sin(log sqrt(2)),` b) `e^((pi)/(4)cos(log sqrt(2))` c) `0` d) none

The value of int_(-pi//2)^(pi//2) sin{log(x+sqrt(x^(2)+1)}dx is

Prove that : int_(0)^(1) (log x)/(sqrt(1-x^(2)))dx=-(pi)/(2)log 2

lim_(xrarroo) x^(2)sin(log_(e)sqrt(cos(pi)/(x)))

lim_(n to oo) x^(2)sin(log_(e)sqrt(cos((pi)/(x)))) is less then

If e^(sin x)-e^(-sin x)-4=0 , then x= (a) 0 (b) sin^(-1){(log)_e(2+sqrt(5))} (c) 1 (d) none of these

Prove that : int_(0)^(pi//2)(x)/(sin x +cos x)dx= (pi)/(4sqrt(2)) log |(sqrt(2)+1)/(sqrt(2)-1)|

5.The modulus amplitude form of -1-i is (a) -sqrt(2)(cos(pi/4)+i sin(pi/4)) (b) sqrt(2)(cos((3pi)/4)+i sin((3pi)/4)) (c) sqrt(2)[cos(-(3 pi)/(4))+i sin(-(3 pi)/(4))] (d) None of these.

The principal value of sin^(-1)(sin((2pi)/3)) is (a) -(2pi)/3 (b) (2pi)/3 (c) (4pi)/3 (d) (5pi)/3 (e) none of these

int_(0)^(pi//2)(dx)/(1+e^(sqrt(2)cos(x+(pi)/(4)))) is equal to

int_0^3(3x+1)/(x^2+9)dx = (pi^)/(12)+log(2sqrt(2)) (b) (pi^)/2+log(2sqrt(2)) (c) (pi^)/6+log(2sqrt(2)) (d) (pi^)/3+log(2sqrt(2))