`int_0^1 cos(pit/2) dt` Evaluate the definite integral.

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Given: `int_0^1cos(pit/2)dt`

Integrate using the u-substitution method.

Let `u=pi/2t`

`(du)/dt=pi/2`

`dt=2/pi*du`

 

`=int_0^1cos(u)*2/pidu`

`=2/piint_0^1cos(u)du`

`=2/pisin(u)`  Evaluated from t=0 to t=1.

`=2/pisin(pi/2t)`  Evaluated from t=0 to t=1.

`=2/pi[sin(pi/2)*1-sin(pi/2)*0]`

`=2/pi[sin(pi/2)-sin0]`

`=2/pi[1-0]`

`=2/pi`

`=.637`

 

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