SOLUTION: 2)what is the value of integration(t*sin(t) dt) from 0 to pi(22/7) by the trapezoidal rule?

Question 33106: 2)what is the value of integration(t*sin(t) dt) from 0 to pi(22/7) by the trapezoidal rule?
Answer by sarah_adam(201) (Show Source): You can put this solution on YOUR website!
We know the formula for integration by parts as
Int(uv) = uv - Int(vdu) over the given interval
so here let u = t and let v= sint
du= dt and dv = -cost + c
now applying the formula we get
Int(tsint) = (tsint) - Int(-cost +c) over the interval of 0 and pi/2
now applying over the interval
{(pi/2*sinpi/2)-0} - {(-cos pi/2 +c) - (-cos 0 +c)}
sin pi/2 = 1 ,cos pi/2 = 0 and cos 0 =1
so the final answer is
pi/2 - (0+c+1-c)
pi/2 - 1
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