The following illustrates the function, y=f(x) for x = 0 to x=10. The curve from x=0 to x=3 Is a part of a circle of radius 3 units, similarly for that part of the curve from x = 3 x = 6 . From x = 6 to x=10, the function is a straight line. Explain why f(x)dx= -6.
The area between the curve and x-axis from x=0 tox=3 is the same as the area between the curve and x-axis fromx=3 to x=6, but since it is below the x-axis here, the value ∫36f(x)dx=-∫03f(x)dx and so they cancel tp zerp when added Similary the area between the curve line y=f(x) from x=6 to x=10 is below hence negative the x-axis and forma triangle area=12×base×height =12(10-6)×3=6 units ∫010f(x)dx=∫03f(x)dx+∫36f(x)dx+∫010f(x)dx=0+-6=-6
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