How do you integrate f(t) = 1.4e^(0.07t)?

Oct 23, 2017

$\int 1.4 {e}^{0.07 t} \mathrm{do} = 20 {e}^{0.07 t}$

Explanation:

$f \left(t\right) = \int 1.4 {e}^{0.07 t} \mathrm{dt}$

$= \left(\frac{7}{5}\right) \int {e}^{\frac{7 t}{100}} \mathrm{dt}$

$u = \frac{7 t}{100} , \mathrm{du} = \left(\frac{7 t}{100}\right) \mathrm{dx} , \mathrm{dx} = \left(\frac{100}{7}\right) \mathrm{du}$

Apply constant multiple rule,

$f \left(t\right) = \left(\cancel{\frac{7}{5}} \cancel{\frac{100}{7}}\right) 20 \int {e}^{u} \mathrm{du}$

$f \left(t\right) = 20 \int {e}^{u} \mathrm{du} = 20 {e}^{u}$

But ${e}^{u} = {e}^{0.07}$

$\therefore \int 1.4 {e}^{0.07 t} \mathrm{dt} = 20 {e}^{0.07 t}$