Answer to Question #101813 in Calculus for Joe

Question #101813
Coordinate axes, the curve y = sin (x) and the straight line x = 3π/2 limit one area.
Determine the size of this area.
1
Expert's answer
2020-01-27T09:27:27-0500

Solution. Sketch the desired area




Using the properties of the integral, the desired area is equal to


"S=\\int _0^\\pi (sin x-0)dx+\\int _\\pi^{\\frac {3\\pi}{2}}(0-sinx)dx"

"S=\\int _0^\\pi sin xdx-\\int _\\pi^{\\frac {3\\pi}{2}}sinxdx"

"S=-cosx|_0^{\\pi}+cosx|_{\\pi}^{\\frac {3\\pi}{2}}=1+1+0+1=3"


Answer. 3.


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