Question

Let be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when Ris revolved about the x-axis. y=19-xy=x, and y=0 Set up the integral that gives the volume of the sold. Use increasing limits of integration Select the correct choice below and fill in the answer boxes to complete your choice. (Type an exact answer OAJO OB The volume is Type an exact now)

Answer 1

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y=x 9-19-x A > at A 19 x = x 2x = 19 x= 19

The volume generated by the region will be two times the volume generated by the area the triangle Since the slopes of y=x curre and y = 19 x qual in opposite directions ABC aus ne au magnitude deut at point x, the area 1 the circle with y value is yo area Tay? the yo value which the same as x, will vary from o 19 for the triangle ABC the summation these areas will constitute the local volume letal volume 19/ V 2 ny²dy. o 192 V Saxda

19/ volune V=2 ñna dn D 19/2 3 1995.68 unit