`int_0^(pi/2) sin^(-1) x dx`

int_(0)^(pi/2) sin^(-1)(sin x)dx

IF int_0^a sqrtx dx=2a int_0^(pi//2) sin^3 x dx, find int_a^(a+1) x dx .

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

int_(0)^(1) sin^(-1) x dx =(pi)/(2) -1

int_0^(pi/2) sin x dx

Sketch the regions represented by the following: (i) int_0^1 x^2 dx (ii) int_0^(pi/2) sin x dx

Evaluate: int_0^(pi/2) (sin2x tan^(-1)(sinx))dx

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

int_0^(pi//2) (sin^(1//2)x)/(sin^(1//2)x+cos^(1//2)x) dx is equal to

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