9. Graphical Applications of Integrals

Finding volume

The region in the first quadrant that is enclosed by the x-axis and the curve y = 3x√(1 − x) is revolved about the y-axis to generate a solid. Find the volume of the solid.

Areas of Surfaces of Revolution

In Exercises 23–26, find the areas of the surfaces generated by revolving the curves about the given axes.

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y = √2x + 1 , 0 ≤ x ≤ 3 ; x-axis"

Areas of Surfaces of Revolution

In Exercises 23–26, find the areas of the surfaces generated by revolving the curves about the given axes.

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y = √4y ― y² , 1 ≤ y ≤ 2 ; y-axis

80. Volume The region enclosed by the curve y=sech(x), the x-axis, and the lines x=±ln√3 is revolved about the x-axis to generate a solid. Find the volume of the solid.

Volume: Find the volume of the solid generated by revolving the region in Exercise 45 about the x-axis.