` int_0^((pi)/4) xsec^2 x dx`

int_0^(pi/4) tan^3xsec^2xdx

(i) int_0^(pi//4) sec x dx (ii) int_(pi//6)^(pi//4) cosec x dx

(i) int_0^(pi/2) sin^2 x dx (ii) int_0^(pi//2) cos^2 x dx

int_0^(pi//2) x^2 cos 2x dx

(i) int_0^(pi//2) sin^2 dx =pi/4 (ii) int_0^(pi//2) cos^2x dx=pi/4 (iii) int_(-pi//4)^(pi//4) sin^2 x dx=pi/4-1/2 (iv) int_(-pi//4)^(pi//4) cos^2x dx=pi/4+1/2

The value of int_0^(pi//4) sqrt(tan x dx) +int_0^(pi//4) sqrt(cot x dx) is equal to

If I = int_(0)^(pi//4) sin^(2) x" "dx and J = int_(0)^(pi//4)cos^(2)x" " dx. then

Evaluate (i) int_0^(pi//4) sin x cos x dx (ii) int_0^(pi//2) (1 + cos x)^(1//2) dx (iii) int_0^(pi//2) (1 + sin x)^(1//2) dx (iv) int_0^(pi//4) (1 -cos 2x)^(1//2)dx

Evaluate int_0^(pi/4) dx/(cos^2x + 4sin^2x)