Evaluate the Integral integral of 2x^2 with respect to x

Problem

(∫_^)(2*x2*d(x))

Solution

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

2. Apply the constant multiple rule for integration by moving the constant 2 outside the integral.

(∫_^)(2*x2*d(x))=2*(∫_^)(x2*d(x))

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

2*(∫_^)(x2*d(x))=2⋅(x(2+1))/(2+1)+C

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

2⋅(x3)/3+C=(2*x3)/3+C

Final Answer

(∫_^)(2*x2*d(x))=(2*x3)/3+C

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