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Iff(x)=int0^pi(tsintdt)/(sqrt(1+tan^2xsi...

`Iff(x)=int_0^pi(tsintdt)/(sqrt(1+tan^2xsin^2t))for0

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If f(x) = int_0^pi (t sint dt) / (sqrt(1+tan^2xsin^2t)) for 0 < x < pi/2 , then (a) f(0^+)=-pi (b) f(pi/4)=(pi^2)/8 (c) f is continuous and differentiable in (0,pi/2) (d) f is continuous but not differentiable in (0,pi/2)

If f(x) = int_0^pi (t sint dt) / (sqrt(1+tan^2xsin^2t)) for 0 < x < pi/2 , then (a) f(0^+)=-pi (b) f(pi/4)=(pi^2)/8 (c) f is continuous and differentiable in (0,pi/2) (d) f is continuous but not differentiable in (0,pi/2)

If f(x)=int_(0)^(pi)(t sin t dt)/(sqrt(1+tan^(2)xsin^(2)t)) for 0lt xlt (pi)/2 then

If f(x)=int_(0)^(pi)(t sin t dt)/(sqrt(1+tan^(2)xsin^(2)t)) for 0lt xlt (pi)/2 then

If f(x)=int_(0)^(pi)(t sin t dt)/(sqrt(1+tan^(2)xsin^(2)t)) for 0lt xlt (pi)/2 then

If f(x)=int_0^(pi/2)ln(1+xsin^2theta)/(sin^2theta) d theta, x >= 0 then :

int_(0)^(pi//2)(1)/(1+sqrt(tan x))dx=

Find the mistake of the following evaluation of the integral I=int_(0)^( pi)(dx)/(1+2sin^(2)x)I=int_(0)^( pi)(dx)/(cos^(2)x+3sin^(2)x)=int_(0)^( pi)(sec^(2)xdx)/(1+3tan^(2)x)=(1)/(sqrt(3))[tan^(-1)(sqrt(3)tan x)]_(0)^( pi)=0

int_(0)^(pi//2)(1)/(sqrt(tan x)-sqrt(cot x))dx=