Area lying between the curves `y=tanx, y=cotx` and x-axis, `x in [0, pi/2]` is (A) `1/2log2` (B) `log2` (C) `2log(1/sqrt(2))` (D) none of these

int_2^4 log[x]dx is (A) log2 (B) log3 (C) log5 (D) none of these

The area between the curves y=ln x and y=(ln x)^(2) is

PROFICIENCY TEST-1The area between the curve xy = a?, x-axis, x = a and x = 2a is lagt(A) a log 2(B) a2 log 2(C) 2a log 2(D) None of theseArea under the cum

int_0^oo logx/(1+x^2)dx= (A) log2 (B) pi/2 (C) 0 (D) none of these

The area bounded by the curve y=secx , the x-axis and the lines x=0 and x=pi/4 is (A) log(sqrt(2)+1) (B) log(sqrt(2)-1) (C) 1/2log2 (D) sqrt(2)

Area of the region bounded by the curves y=2^x, y=2x-x^2, x=0 and x=2 is given by (A) 3log2-4/3 (B) 3/log2-4/3 (C) 3log2+4/3 (D) 3/log2+4/3

The function f is such that : f(xy)=f(x)+f(y), x, y gt 0 and f\'(1)=2 and A the area bounded by the curves y=f(x), x=2 and the x-axis, then (A) f(x)=2log_ex (B) f(x)=2 log_ex (C) A=2(2log_e2-1) (D) A=4log(2/sqrt(e))

The area bounded by the curve y=2^(x), the x- axis and the left of y-axis is (A) log _(e)2(B)log_(e)4 (C) log_(4)e(D)log_(2)e