Math Is Fun Forum

not sure if this is the correct section to post but seemed most suitable to me...please move if needed.

here's the problem integral problem

the way i've been doing it, and the way i want to is to find the antiterivative and then sub in the limits, however, have some trouble doing so.
i'l use '~' as the integral symbol
and 'sqrt' as square root symbol

first i let u = sinx   where du=cosxdx
therefore

=-sinx 0~1/2 sqrt(u)*du       if x=0, u=0      if x=1/2, u=0.009

= -sinx 0~0.009 u^1/2*du

=-sinx [2/3U^2/3]

=[-sinx(2/3sinx^3/2)]

and the answers are completely wrong. i have check it on my calculator and it should be 0.031 or thereabouts.

secondly, solving the systems using the Gaussian elimination method, i haven't been able to come across any results that satisfy and of the equations.

here is the equations giving me trouble

and here is what i worked out

  2 4 -6, 2           1 0 4, 6         1 0 4, 6           1 0 4, 6          1 0 0,-98
[ 0 1 2,  4 ]  ~  [ 0 1 2, 4 ]  ~  [0 1 2, 4 ]  ~  [ 0 1 2, 4 ]  ~  [0 1 0, 75/22]
  1 0 4, -6           2 4 -6, 2        0 4 -14, -10     0 0 -22, -26    0 0 1, 13/11

if someone could smash up what they thinks right, thatd be awesome as i'm just blind to what i've done wrong (most people are to their own mistakes!), or how i should go about it. these are the methods i need to use to solve them to so please dont smash up easier ways, i'd be using them if i could!
thanks,
dave