Evaluate the Integral

Problem

(∫_0^2)(x*d(x))

Solution

1. Identify the integrand and the limits of integration. The function to integrate is ƒ(x)=x and the interval is [0,2]

2. Apply the power rule for integration, which states that (∫_^)(xn*d(x))=(x(n+1))/(n+1) For n=1 the antiderivative is (x2)/2

3. Evaluate the antiderivative at the upper limit of integration (x=2 and the lower limit of integration (x=0.

F(2)=2/2=4/2=2

F(0)=0/2=0

4. Subtract the value at the lower limit from the value at the upper limit according to the Fundamental Theorem of Calculus.

2−0=2

Final Answer

(∫_0^2)(x*d(x))=2

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