Evaluate the Integral

Problem

(∫_−6^7)(x*d(x))

Solution

1. Identify the integrand and the limits of integration. The function is ƒ(x)=x the lower limit is a=−6 and the upper limit is b=7

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 and lower limits: F(7)−F*(−6)

4. Substitute the values into the expression: ((7)2)/2−((−6)2)/2

5. Simplify the arithmetic: 49/2−36/2=13/2

Final Answer

(∫_−6^7)(x*d(x))=13/2

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