Evaluate Integral: Get Help Now!

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The integral evaluation discussed involves the computation of the integral ∞ ∫0.2e^−0.2u du. By substituting t = 0.2u, the limits of integration are adjusted, leading to the expression ∞ ∫2 e^−t dt. The evaluation results in the limit as b approaches infinity, yielding a final answer of 1/e². This method demonstrates the application of substitution in integral calculus effectively.

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

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

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

substitute and reset the limits of integration

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

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

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

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