Evaluate the Integral

Problem

(∫_−1^1)(x*d(x))

Solution

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

2. Apply the Power Rule for integration, which states that (∫_^)(xn*d(x))=(x(n+1))/(n+1)

3. Find the antiderivative of x which is (x2)/2

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

5. Substitute the values: ((1)2)/2−((−1)2)/2

6. Simplify the arithmetic expression to find the final value.

Final Answer

(∫_−1^1)(x*d(x))=0

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