Evaluate the Integral

Problem

(∫_0^2)(e^x*d(x))

Solution

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

2. Find the antiderivative of the function e^x The antiderivative of e^x is e^x

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)(e^x*d(x))=[e^x]^2_0

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

e^2−e^0

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

e^2−1

Final Answer

(∫_0^2)(e^x*d(x))=e^2−1

Want more problems? Check here!