Evaluate the Integral integral of e^(-2t) with respect to t

Problem

(∫_^)(e(−2*t)*d(t))

Solution

1. Identify the form of the integral, which is an exponential function of the form (∫_^)(e(a*t)*d(t))

2. Apply the rule for integrating exponential functions, where (∫_^)(e(a*t)*d(t))=1/a*e(a*t)+C

3. Substitute the constant a=−2 into the formula.

4. Simplify the expression and add the constant of integration C

Final Answer

(∫_^)(e(−2*t)*d(t))=−1/2*e(−2*t)+C

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