Question Number 143372 by mohammad17 last updated on 13/Jun/21
Commented by mohammad17 last updated on 13/Jun/21
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Answered by bramlexs22 last updated on 13/Jun/21
![(1) vol = π∫_0 ^4 [(2)^2 −((√x))^2 ] dx = π [ 4x−(1/2)x^2 ]_0 ^4 = 8π (2) vol = π ∫_0 ^( 2) y^4 dy = ((32π)/5)](Q143374.png)
$$\left(\mathrm{1}\right)\:{vol}\:=\:\pi\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\:\left[\left(\mathrm{2}\right)^{\mathrm{2}} −\left(\sqrt{{x}}\right)^{\mathrm{2}} \right]\:{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\pi\:\left[\:\mathrm{4}{x}−\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{2}} \:\right]_{\mathrm{0}} ^{\mathrm{4}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{8}\pi\: \\ $$$$\left(\mathrm{2}\right)\:{vol}\:=\:\pi\:\int_{\mathrm{0}} ^{\:\mathrm{2}} \:{y}^{\mathrm{4}} \:{dy}\:=\:\frac{\mathrm{32}\pi}{\mathrm{5}} \\ $$
Commented by mohammad17 last updated on 13/Jun/21
$${and}\:\left(\mathrm{3}\right)\:,\:\left(\mathrm{4}\right)\:{sir} \\ $$