Evaluate the Integral integral of e^(-3t) with respect to t

Problem

(∫_^)(e(−3*t)*d(t))

Solution

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

2. Apply the rule for integrating an exponential function where the exponent is a linear function of the variable.

3. Divide the expression by the coefficient of t which is −3

4. Add the constant of integration C to complete the indefinite integral.

Final Answer

(∫_^)(e(−3*t)*d(t))=−1/3*e(−3*t)+C

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