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

Problem

(∫_^)(e(−t)*d(t))

Solution

1. Identify the form of the integral, which is an exponential function with a linear exponent of the form e(a*t)

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

3. Substitute the value a=−1 into the formula.

4. Simplify the expression by dividing by −1

Final Answer

(∫_^)(e(−t)*d(t))=−e(−t)+C

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