Evaluate the Integral

Problem

(∫_0^4)(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 [0,4]

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

F(4)−F(0)=4/2−0/2

4. Simplify the resulting numerical expression.

16/2−0=8

Final Answer

(∫_0^4)(x*d(x))=8

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