Evaluate the Integral integral of 15x^(1/2) with respect to x

Problem

(∫_^)(15*x(1/2)*d(x))

Solution

1. Identify the constant and the power of x in the integrand.

2. Apply the constant multiple rule by moving the coefficient 15 outside the integral.

15*(∫_^)(x(1/2)*d(x))

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

15⋅(x(1/2+1))/(1/2+1)+C

4. Simplify the exponent and the denominator.

15⋅(x(3/2))/(3/2)+C

5. Multiply by the reciprocal of the denominator to simplify the expression.

15⋅2/3*x(3/2)+C

6. Calculate the final coefficient.

10*x(3/2)+C

Final Answer

(∫_^)(15*x(1/2)*d(x))=10*x(3/2)+C

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