Question Number 132643 by aurpeyz last updated on 15/Feb/21
Commented by mr W last updated on 15/Feb/21
$${question}\:{not}\:{clear}! \\ $$$$…\:{t}=\mathrm{1}\:{and}\:{what}? \\ $$
Commented by aurpeyz last updated on 15/Feb/21
$${t}={e}^{{t}} \\ $$
Commented by mr W last updated on 15/Feb/21
$${t}={e}^{{t}} \:{makes}\:{no}\:{sense}.\:{from}\:{t}=\mathrm{1}\:{to} \\ $$$${t}=××,\:××\:{must}\:{be}\:{a}\:{value}! \\ $$
Commented by mr W last updated on 15/Feb/21
$${a}\:{terrible}\:{book}\:{with}\:{so}\:{many}\: \\ $$$${errors}\:{even}\:{in}\:{one}\:{single}\:{question}! \\ $$
Commented by aurpeyz last updated on 16/Feb/21
$${the}\:{textbook}\:{is}\:{terrible}\:{Sir}. \\ $$
Answered by mr W last updated on 15/Feb/21
![assume t=1 to t=e v=(ds/dt)=(1/t)+t Δs=∫_1 ^e ((1/t)+t)dt =[ln t+(t^2 /2)]_1 ^e =ln e+(e^2 /2)−(ln 1+(1^2 /2)) =((1+e^2 )/2)](https://www.tinkutara.com/question/Q132680.png)
$${assume}\:{t}=\mathrm{1}\:{to}\:{t}={e} \\ $$$${v}=\frac{{ds}}{{dt}}=\frac{\mathrm{1}}{{t}}+{t} \\ $$$$\Delta{s}=\int_{\mathrm{1}} ^{{e}} \left(\frac{\mathrm{1}}{{t}}+{t}\right){dt} \\ $$$$=\left[\mathrm{ln}\:{t}+\frac{{t}^{\mathrm{2}} }{\mathrm{2}}\right]_{\mathrm{1}} ^{{e}} \\ $$$$=\mathrm{ln}\:{e}+\frac{{e}^{\mathrm{2}} }{\mathrm{2}}−\left(\mathrm{ln}\:\mathrm{1}+\frac{\mathrm{1}^{\mathrm{2}} }{\mathrm{2}}\right) \\ $$$$=\frac{\mathrm{1}+{e}^{\mathrm{2}} }{\mathrm{2}} \\ $$
Commented by aurpeyz last updated on 16/Feb/21
$${thank}\:{you}\:{so}\:{much} \\ $$