Question

Ache a área sobre o gráfico de f(x) = 1/x e o eixo x, entre x = e e x = e².

Answer 1

Resposta:

Área = 1 u²

Explicação passo-a-passo:

$\displaystyle\int_{e}^{e^2}\frac{1}{x}~dx=|lnx|]_e^e^{^{2} }=|lne^2-lne|=|2lne-lne|=|lne|=|1|=1$

Answer 2

$\large\boxed{\begin{array}{l}\underline{\rm observe~a~figura~que~anexei}\\\sf a~\acute area~da~regi\tilde ao~\acute e~dada~por\\\displaystyle\sf A=\int _e^{e^2}\dfrac{1}{x}~dx\\\sf A=\bigg[\ell n|x|\bigg]_e^{e^2}\\\sf como~os~limites~de~integrac_{\!\!,}\tilde ao~s\tilde ao~positivos,\\\sf podemos~tirar~o~m\acute odulo.~desta~forma~temos:\\\sf A=\bigg[\ell n x\bigg]_e^{e^2}\\\sf A=\ell n e^2-\ell ne\\\sf usando~a~propriedade~\ell n a-\ell nb=\ell n\bigg(\dfrac{a}{b}\bigg)\end{array}}$

$\large\boxed{\begin{array}{l}\sf A=\ell n\bigg(\dfrac{e^2}{e}\bigg)\\\sf A=\ell n e^{2-1}\\\sf A=\ell ne\\\sf A=1~u\cdot a\end{array}}$