Find the Integral e^(-3t)

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 with a linear exponent, which states (∫_^)(e(a*t)*d(t))=1/a*e(a*t)+C

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

4. Simplify the expression by placing the negative sign in front of the fraction.

Final Answer

(∫_^)(e(−3*t)*d(t))=−1/3*e(−3*t)+C

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