Question Number 174576 by othman last updated on 04/Aug/22
Answered by Ar Brandon last updated on 04/Aug/22
![t=w^2 −4 ⇒dt=2wdw 2∫_(−3) ^0 (1/( (t)^(1/3) ))dt=3[t^(2/3) ]_(−3) ^0 =−3(9)^(1/3)](Q174577.png)
$${t}={w}^{\mathrm{2}} −\mathrm{4}\:\Rightarrow{dt}=\mathrm{2}{wdw} \\ $$$$\mathrm{2}\int_{−\mathrm{3}} ^{\mathrm{0}} \frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{t}}}{dt}=\mathrm{3}\left[{t}^{\mathrm{2}/\mathrm{3}} \right]_{−\mathrm{3}} ^{\mathrm{0}} =−\mathrm{3}\sqrt[{\mathrm{3}}]{\mathrm{9}} \\ $$