Evaluate the Integral integral of x^(1/2) with respect to x

Problem

(∫_^)(x(1/2)*d(x))

Solution

1. Identify the form of the integral as a power function, where the integrand is xn with n=1/2

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

3. Substitute n=1/2 into the formula to get (x(1/2+1))/(1/2+1)+C

4. Simplify the exponent and the denominator by calculating 1/2 + 1 = 3/2$.

5. Finalize the expression by multiplying by the reciprocal of the denominator.

Final Answer

(∫_^)(x(1/2)*d(x))=(2*x(3/2))/3+C

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