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Find the antiderivative of

f(x) = 3x^2

Jan 3, 2024

Find the antiderivative of

f(x) = 3x^2

Solution by Steps

step 1

To find the antiderivative of

f(x) = 3x^2

, we apply the power rule for antiderivatives, which states that the antiderivative of

x^n

\frac{x^{n+1}}{n+1}

, provided

n \neq -1

step 2

Applying the power rule to

3x^2

, we increase the exponent by 1 to get

x^{2+1}

and divide by the new exponent,

3

. This gives us

\frac{3x^{3}}{3}

step 3

Simplifying the expression from step 2, we get

x^3

step 4

Don't forget to add the constant of integration,

C

, to the antiderivative

Answer

The antiderivative of

f(x) = 3x^2

x^3 + C

Key Concept

Power Rule for Antiderivatives

Explanation

The power rule for antiderivatives is used to integrate polynomials. For

f(x) = x^n

, the antiderivative is

\frac{x^{n+1}}{n+1} + C

, where

C

is the constant of integration.