Evaluate the Integral

Problem

(∫_−1^−1)(4*x−4*d(x))

Solution

1. Identify the limits of integration for the definite integral.

2. Observe that the lower limit of integration is a=−1 and the upper limit of integration is b=−1

3. Apply the property of definite integrals which states that if the upper and lower limits are equal, the integral is zero:

(∫_a^a)(ƒ(x)*d(x))=0

4. Conclude that since the limits are identical, the area under the curve is zero regardless of the integrand.

Final Answer

(∫_−1^−1)(4*x−4*d(x))=0

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