Find the Antiderivative f(x)=3x^2

Problem

(∫_^)(3*x2*d(x))

Solution

1. Identify the function to be integrated, which is ƒ(x)=3*x2

2. Apply the constant multiple rule for integration, which allows the constant 3 to be moved outside the integral.

(∫_^)(3*x2*d(x))=3*(∫_^)(x2*d(x))

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

3*(∫_^)(x2*d(x))=3⋅(x(2+1))/(2+1)+C

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

3⋅(x3)/3+C

5. Cancel the common factor of 3 in the numerator and denominator.

x3+C

Final Answer

(∫_^)(3*x2*d(x))=x3+C

Want more problems? Check here!