Solutions - 0030-02

You can set up each integral using disks/washers or using shells.

(1) Using washers, obtain:

V \;=\; \int_0^\sqrt{2}\pi(4-x^2)^2-\pi\, 2^2\,dx ParseError: Got function '\sqrt' with no arguments as superscript at position 16: V \;=\; \int_0^\̲s̲q̲r̲t̲{2}\pi(4-x^2)^2…

Using shells, obtain:

$$V={\int }_2^{4}2\pi y\sqrt{4-y}dy$$

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(2) Using disks, obtain:

$$V={\int }_2^4\pi {\left(\sqrt{4-y}\right)}^{2}dy$$

Using shells, obtain:

V \;=\; \int_0^\sqrt{2} 2\pi x\left((4-x^2)-2\right)\,dx ParseError: Got function '\sqrt' with no arguments as superscript at position 16: V \;=\; \int_0^\̲s̲q̲r̲t̲{2} 2\pi x\left…