Evaluate the Integral integral of x/2 with respect to x

Problem

(∫_^)(x/2*d(x))

Solution

1. Identify the constant factor in the integrand. The expression x/2 can be rewritten as 1/2⋅x

2. Apply the constant multiple rule for integration, which allows the constant 1/2 to be moved outside the integral sign.

(∫_^)(1/2*x*d(x))=1/2*(∫_^)(x*d(x))

3. Apply the power rule for integration, (∫_^)(xn*d(x))=(x(n+1))/(n+1) where n=1

(∫_^)(x1*d(x))=(x(1+1))/(1+1)=(x2)/2

4. Multiply the result by the constant factor 1/2 and add the constant of integration C

1/2⋅(x2)/2+C=(x2)/4+C

Final Answer

(∫_^)(x/2*d(x))=(x2)/4+C

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