Need complete solutions to these questions.Thanks in advance.

1, Find the Hermite interpolation polynomial for f(x) with f(1)=2. f(2)=3. and f'('l)=0, f'(2)=-'l. Be sure to show your work. 2, Verify that the integral of the following functions are zero on the interval from 0 to 2'\"\\pi, (a) sin(kx)cos(jx) and any k and j; (b) sin(kx)sin(ix) for] not equal to k. How about the integral of sin(kx)sin(kx) from 0 to 2"\\pi. Review some trigonometric formula if necessary