integration

[maney21]

what is the integration of 20sinpi t/30 where t=0 to t=1

 

[galactus]

Please use proper grouping symbols. What is that?.

Is it $\displaystyle 20sin(\frac{{\pi}t}{30}) \;\ or \;\ \frac{20sin({\pi}t)}{30}$

 

[maney21]

20 sin(pit/30) where t=0 to t=1.................please if possible i need the answer soon ................once again thank you so much

 

[maney21]

1st one

 

[BigGlenntheHeavy]

$\displaystyle \int_{0}^{1}20sin\bigg(\frac{\pi t}{30}\bigg)dt \ = \ 20\int_{0}^{1}sin\bigg(\frac{\pi t}{30}\bigg)dt$

$\displaystyle Now \ let \ u \ = \ \frac{\pi t}{30}, \ du \ = \ \frac{\pi dt}{30}, \ \frac{30du}{\pi} \ = \ dt$

$\displaystyle Ergo, \ we \ have: \ 20\bigg(\frac{30}{\pi}\bigg)\int_{0}^{\pi/30}sin(u)du \ = \ \frac{600}{\pi}\bigg[-cos(u)\bigg]_{0}^{\pi/30}$

$\displaystyle = \ \frac{600}{\pi}[1-cos(\pi/30)] \ = \ 1.0462409171$