Question Number 42713 by Rio Michael last updated on 01/Sep/18
Commented by Rio Michael last updated on 01/Sep/18
$${find}\:{the}\:{Area}\:{bounded}\:{by}\:{the}\:{curve}\:{y}=\:{x}^{\mathrm{2}} ,{the}\:{x}−{axis}\:{and}\: \\ $$$${the}\:{line}\:{x}=\mathrm{2}. \\ $$
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](Q42715.png)
$${Required}\:{Area}=\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}{x}^{\mathrm{2}} {dx} \\ $$$$=\left[\frac{{x}^{\mathrm{3}} }{\mathrm{3}}\underset{\mathrm{0}} {\overset{\mathrm{2}} {\right]}} \\ $$$$=\frac{\mathrm{2}^{\mathrm{3}} }{\mathrm{3}} \\ $$$$=\frac{\mathrm{8}}{\mathrm{3}}{sq}.\:{unit} \\ $$