Question 345256
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Just divide your integral into two separate parts and add the two.


*[tex \LARGE\ \ \ \ \ \ \ \ \ \ \int_{0}^{\frac{3\pi}{2}}\ f(x)\,dx\text{  where  }f(x)\ =\ \left\{\sin(x)\text{  if  }0\ \leq\ x\ <\ \frac{\pi}{2}\cr\ \ \ \ \ \ \ 1\text{  if  }\frac{\pi}{2}\ \leq\ x\ \leq\ \frac{3\pi}{2}]


can be written as:


*[tex \LARGE\ \ \ \ \ \ \ \ \ \ \int_{0}^{\frac{\pi}{2}}\ \sin(x)\,dx\ +\ \int_{\frac{\pi}{2}}^{\frac{3\pi}{2}}\ \,dx]


*[tex \LARGE\ \ \ \ \ \ \ \ \ \  -cos(x)\,|_{0}^{\frac{\pi}{2}}\ +\ x\,|_{\frac{\pi}{2}}^{\frac{3\pi}{2}}]


*[tex \LARGE\ \ \ \ \ \ \ \ \ \  0\ -\ (-1)\ +\ \left(\frac{3\pi}{2}\ -\ \frac{\pi}{2}\right)\ =\ 1\ +\ \pi]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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