Question Number 148905 by DELETED last updated on 01/Aug/21
Answered by DELETED last updated on 01/Aug/21
![Answered: −∫_2 ^4 (x^2 −5x )dx=− [(1/3)x^3 −(5/2)x^2 ] _2 ^4 = −[{((64)/3) − ((80)/2) }−{(8/3) − ((20)/2)} ] =−((56)/3) +((90)/3) = ((34)/3) = 11,33 unit^2 //](https://www.tinkutara.com/question/Q148907.png)
$$\mathrm{Answered}: \\ $$$$−\underset{\mathrm{2}} {\overset{\mathrm{4}} {\int}}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{5x}\:\right)\mathrm{dx}=−\:\left[\frac{\mathrm{1}}{\mathrm{3}}\mathrm{x}^{\mathrm{3}} −\frac{\mathrm{5}}{\mathrm{2}}\mathrm{x}^{\mathrm{2}} \right]\underset{\mathrm{2}} {\overset{\mathrm{4}} {\:}} \\ $$$$=\:−\left[\left\{\frac{\mathrm{64}}{\mathrm{3}}\:−\:\frac{\mathrm{80}}{\mathrm{2}}\:\right\}−\left\{\frac{\mathrm{8}}{\mathrm{3}}\:−\:\frac{\mathrm{20}}{\mathrm{2}}\right\}\:\right] \\ $$$$=−\frac{\mathrm{56}}{\mathrm{3}}\:+\frac{\mathrm{90}}{\mathrm{3}}\:=\:\frac{\mathrm{34}}{\mathrm{3}}\:=\:\mathrm{11},\mathrm{33}\:\mathrm{unit}^{\mathrm{2}} // \\ $$$$ \\ $$