SOLUTION: Please help me solve this equation: {{{ int( f(x), dx, 0, 3pi/2 ) where f(x)= system( sin(x) if 0<=x<pi/2, (1) if (pi/2)<=x<=3pi/2 )}}}
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Question 345256: Please help me solve this equation:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Just divide your integral into two separate parts and add the two.
\,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:
\,dx\ +\ \int_{\frac{\pi}{2}}^{\frac{3\pi}{2}}\ \,dx)
\,|_{0}^{\frac{\pi}{2}}\ +\ x\,|_{\frac{\pi}{2}}^{\frac{3\pi}{2}})
\ +\ \left(\frac{3\pi}{2}\ -\ \frac{\pi}{2}\right)\ =\ 1\ +\ \pi)
John
My calculator said it, I believe it, that settles it
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