`int_0^1 (tan^-1x)/xdx-1/2int_0^(pi/2) t/sint dt` has the value (A) `-1` (B) `1` (C) `2` (D) `0`

int_0^1 tan^-1xdx

I=int_(0)^(1)tan^(-1)xdx

Show that: int_0^1 tan^-1x/xdx=1/2int_0^(pi/2) ycosecy dy

int_0^1 x^2e^xdx

int_0^(pi/2)1/(1+tan^2x)dx

If int_0^xf(t) dt=x+int_x^1 tf(t)dt, then the value of f(1)

f(x)=int_0^x f(t) dt=x+int_x^1 tf(t)dt, then the value of f(1) is

Let a=int_0^(pi/2) sinx/xdx , then (A) 0ltalt1 (B) agt2 (C) 1ltaltpi/2 (D) none of these

lim_(xto oo) (int_(0)^(x)(tan^(-1)t)^2dt)/(sqrt(x^(2)+1)) has the value a)zero (b) pi/4 (c) 1 (d) (pi^2)/4

If f(x)=int_0^x(sint)/t dt ,x >0, then