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Evaluate : int(pi/6)^(pi/3)(dx)/(1+sqr...

Evaluate : `int_(pi/6)^(pi/3)(dx)/(1+sqrt(cotx))`

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int_(pi/6)^(pi/3) (dx)/(1+sqrtcotx) =

int_(pi//6)^(pi//3) (dx)/(1 + sqrt(tan x)) =

Evaluate pi_(pi/6)^(pi/3)(dx)/(1+sqrt(tanx))

a) Prove that int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx" and evaluate "int_(pi//6)^(pi//3)(dx)/(1+sqrt(tanx)) b) Prove that |{:(1+a^(2)-b^(2), 2ab, -2b), (2ab, 1-a^(2)+b^(2), 2a), (2, -2a, 1-a^(2)-b^(2)):}|=(1+a^(2)+b^(2))^(3)

Prove that int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx and hence evaluate int_((pi)/(6))^((pi)/(3))(1)/(1+sqrt(tanx))dx.

Evaluate int_(pi//6)^(pi//4)cosecxdx

Evaluate int _(0)^(pi//2)(dx)/(1+ cos x)

Evaluate : int_(-pi/2) ^(pi/2) sin^2x dx