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" 13."int(0)^( pi/4)(sqrt(tan x))dx...

" 13."int_(0)^( pi/4)(sqrt(tan x))dx

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

int_(0)^(pi//4)sqrt(1+cos2x)dx

int_(0)^((pi)/(4))sqrt(1+sin2x)dx

Prove that: int_(0)^((pi)/(4))(sqrt(tan x)+sqrt(cot x)dx=sqrt(2)*(pi)/(2)

Show that int_(0)^(pi//4) (sqrt(tan x )+sqrt(cot x))dx= pi/sqrt(2)

Evaluate int_(0)^((pi)/(4))(sqrt(tan x)+sqrt(cot x))dx

The value of int_(0)^(pi/4) sqrt(tanx) dx+int_(0)^(pi/4) sqrt(cotx) dx is equal to

int_(0)^( pi/4)tan^(3)dx

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