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 exponent 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. Add one to the exponent: −1/2+1=1/2

4. Divide by the new exponent: (x(1/2))/(1/2)

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

6. Add the constant of integration C

Final Answer

(∫_^)(x(−1/2)*d(x))=2*x(1/2)+C

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