Mathematics

# Solve:$\displaystyle \int_{0}^{T/2}{I_{0}\sin(wt)dt}$

##### SOLUTION
$\int_{0}^{T/2}I_{0} sin(wt).dt$
$=I_{0}\int_{0}^{T/2} sin (wt).dt$
$=I_{0}[\frac{-cos\, wt}{w}]_{0}^{T/2}$
$= \frac{I_{0}}{w}[- cos\, w.\frac{T}{2}-(-cos 0)]$
$= \frac{I_{0}}{w}[-cos(\frac{2\pi }{T}.\frac{T}{2})+cos 0]$
$= \frac{I_{0}}{w}[- cos\pi + cos0]$
$= \frac{I_{0}}{w}[I+1]$
$= \frac{2I_{0}}{w}$
$= \frac{2I_{0}}{(\frac{2\pi }{T})}$
$= \frac{T.I_{0}}{\pi }$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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