Find the Integral x/2

Problem

(∫_^)(x/2*d(x))

Solution

1. Rewrite the integrand by pulling out the constant factor of 1/2 to make the integration easier.

1/2*(∫_^)(x*d(x))

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

1/2⋅(x(1+1))/(1+1)

3. Simplify the expression by performing the addition in the exponent and the denominator.

1/2⋅(x2)/2

4. Multiply the fractions and add the constant of integration C

(x2)/4+C

Final Answer

(∫_^)(x/2*d(x))=(x2)/4+C

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