`int_(0)^(1)sin x dx`

prove that: int_(0)^(1)x^2sin x dx >= (2/9)

3.quad int_(0)^(1)|sin2 pi x|dx is equal to-

int_(0)^(1)x sin(x-1)dx+int_(0)^(1)(1-x)sin xdx=

int_(0)^(1) |sin 2pi x|dx id equal to

If int_(0)^(1)(sin x)/(1+x)dx=K the the value of int_(4 pi-2)^(4 pi)(sin((x)/(2)))/(4 pi+2-x)dx equals

Let I=int_(0)^(1) (sin x)/(sqrt(x))dx and I=int_(0)^(1) (cos x)/(sqrt(x))int dx . Then, which one of the following is true?

int_ (0) ^ (1) sin (x ^ (2) + 2x + 1) dx-int_ (1) ^ (2) sin x ^ (2) dx is

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