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.