Evaluate the Integral

Problem

(∫_0^2)(ƒ(x)*d(x))

Solution

1. Identify the integral as a definite integral of a general function ƒ(x) over the interval [0,2]

2. Apply the Fundamental Theorem of Calculus, which states that if F(x) is an antiderivative of ƒ(x) then the integral is calculated by evaluating F(x) at the upper and lower limits.

3. Evaluate the difference between the antiderivative at the upper limit x=2 and the lower limit x=0

Final Answer

(∫_0^2)(ƒ(x)*d(x))=F(2)−F(0)

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