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

Problem

(∫_^)((x2)/2*d(x))

Solution

1. Identify the constant factor in the integrand. The expression (x2)/2 can be written as 1/2⋅x2

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

1/2*(∫_^)(x2*d(x))

3. Apply the power rule for integration, (∫_^)(xn*d(x))=(x(n+1))/(n+1) where n=2

1/2⋅(x(2+1))/(2+1)+C

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

1/2⋅(x3)/3+C

5. Multiply the fractions to find the final result.

(x3)/6+C

Final Answer

(∫_^)((x2)/2*d(x))=(x3)/6+C

Want more problems? Check here!