Evaluate the Integral

Problem

(∫_0^1)(ex*d(x))

Solution

1. Identify the integrand and the limits of integration. The function to integrate is ex and the interval is [0,1]

2. Find the antiderivative of ex The antiderivative of ex is ex

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

[ex]10

4. Substitute the values into the expression.

e1−e0

5. Simplify the result using the properties of exponents, where e1=e and e0=1

e−1

Final Answer

(∫_0^1)(ex*d(x))=e−1

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