Evaluate the Integral

Problem

(∫_0^2)(ex*d(x))

Solution

1. Identify the integrand and the limits of integration. The function to integrate is ex and the interval is [0,2]

2. Find the antiderivative of the function 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 value at the lower limit.

(∫_0^2)(ex*d(x))=[ex]20

4. Substitute the values 2 and 0 into the expression.

e2−e0

5. Simplify the expression using the property that any non-zero number raised to the power of 0 is 1

e2−1

Final Answer

(∫_0^2)(ex*d(x))=e2−1

Want more problems? Check here!