Evaluate the Integral

Problem

(∫_0^8)(e(−x)*d(x))

Solution

1. Identify the antiderivative of the integrand e(−x) using the rule (∫_^)(e(a*x)*d(x))=1/a*e(a*x)

2. Apply the rule with a=−1 to find the indefinite integral.

(∫_^)(e(−x)*d(x))=−e(−x)

3. Apply the Fundamental Theorem of Calculus by evaluating the antiderivative at the upper limit 8 and the lower limit 0

[−e(−x)]80

4. Substitute the limits into the expression.

−e(−8)−(−e0)

5. Simplify the expression using the fact that e0=1

−e(−8)+1

6. Rearrange the terms for the final result.

1−e(−8)

Final Answer

(∫_0^8)(e(−x)*d(x))=1−e(−8)

Want more problems? Check here!