# FIGURE 171283 /3bortio 9rgola aed OFor another method see Exercise 64.6.2 EXERCISES15. y x1-18 Find the volume of the solid obtained by rotating the regionbounded by the given curves about the specified line. Sketch theregion, the solid, and a typical disk or washer.16. xy = 1,17. x = y'1. yx+ 1, y = 0, x = 0, x = 2; about the x-axis18. y x,2. y 1/x, y = 0, x = 1, x = 4; about the x-axis3. y x1, y = 0, x= 5; about the x-axis19-30 Refee, y= 0, x = -1, x = 1; about the x-axis4. yrotating the5. x 2y, x = 0, y 9; about the y-axis0:6. 2x y, x = 0, y 4; about the y-axis7. y x, y= x, x > 0; about the x-axis6 x, y = 2; about the x-axis8. yx, x = 2y; about the y-axis9. y10. x 2 y, x= y; about the y-axis11. y x, x= y; about y = 11, x = 2; about y -312. y x, y19. R1 ab13. y 1sec x, y 3; about y 121. Ri ab14. y sin x, y = cos x, 0 < xTT/4; about y = -1

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Asked Sep 9, 2019
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Step 1

Refer to the question.

We have to find the volume of the solid obtained by revolving y=x3 ,y=x , x=>0 about x axis.

The formula for the volume generated by rotating the region bounded by the given curves about x axis is,

Step 2

Now sketch the graphs of the given curves and find the intersecting points as,

Step 3

So the graph is as follows co...

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