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Question Number 42713 by Rio Michael last updated on 01/Sep/18

Commented by Rio Michael last updated on 01/Sep/18

find the Area bounded by the curve y= x^2 ,the x−axis and   the line x=2.

$${find}\:{the}\:{Area}\:{bounded}\:{by}\:{the}\:{curve}\:{y}=\:{x}^{\mathrm{2}} ,{the}\:{x}−{axis}\:{and}\: \\ $$$${the}\:{line}\:{x}=\mathrm{2}. \\ $$

Answered by $@ty@m last updated on 01/Sep/18

Required Area=∫_0 ^2 x^2 dx  =[(x^3 /3)]_0 ^2   =(2^3 /3)  =(8/3)sq. unit

$${Required}\:{Area}=\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}{x}^{\mathrm{2}} {dx} \\ $$$$=\left[\frac{{x}^{\mathrm{3}} }{\mathrm{3}}\underset{\mathrm{0}} {\overset{\mathrm{2}} {\right]}} \\ $$$$=\frac{\mathrm{2}^{\mathrm{3}} }{\mathrm{3}} \\ $$$$=\frac{\mathrm{8}}{\mathrm{3}}{sq}.\:{unit} \\ $$

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