Evaluate the integral from 0.2 to 10 of 0.2e^−0.2u du

[Lhh]

Can someone help me with this? Not sure where to start.

Exercise 1 (integration) Evaluate the integral
∞
∫0.2e^−0.2u du.
10

 

[skeeter]

$t = 0.2u \implies dt = 0.2 \, du$

substitute and reset the limits of integration

$\displaystyle \lim_{b \to \infty} \int_{2}^b e^{-t} \, dt$

$\displaystyle \lim_{b \to \infty} \bigg[-e^{-t} \bigg]_2^b$

$\displaystyle -\lim_{b \to \infty} \bigg[e^{-b} - e^{-2} \bigg] = -\bigg[0 - \dfrac{1}{e^2} \bigg] = \dfrac{1}{e^2}$