int pi(3x^(2)+2x+3)dx

The value of int_(0)^(2) 3x^(2)dx+int_(0)^(pi//2) sin x dx is :-

(i) int_(0)^(pi//2) x sin x cos x dx (ii) int_(0)^(pi//6) (2+3x^(2)) cos 3x dx

u,=int_(0)^((pi)/(2))cos((2 pi)/(3)sin^(2)x)dx and v,=int_(0)^((pi)/(2))cos((pi)/(3)sin x)dx

Evaluate : int_((pi)/(6))^((pi)/(3)) sin^(2) x dx

int_(pi//3)^(pi//2) dx/(sinx+ sin 2x)=

1) int_(-(pi)/(2))^(pi)sin^(-1)(sin x)dx 2) int_(-(pi)/(2))^((pi)/(2))(-(pi)/(2))/(sqrt(cos x sin^(2)x))dx 3) int_(0)^(2)2x[x]dx