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Answer from Sia

Posted 6 months ago

Solution by Steps

step 1

To find the antiderivative of $f(x) = 3x^2$, we need to integrate the function with respect to $x$

step 2

The integral of $3x^2$ with respect to $x$ is given by $\int 3x^2 \, dx$

step 3

Using the power rule for integration, $\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$, we get $\int 3x^2 \, dx = 3 \cdot \frac{x^{2+1}}{2+1} + C$

step 4

Simplifying, we obtain $3 \cdot \frac{x^3}{3} + C = x^3 + C$

Answer

The antiderivative of $f(x) = 3x^2$ is $x^3 + C$.

Key Concept

Antiderivative (Indefinite Integral)

Explanation

The antiderivative of a function is found by integrating the function with respect to its variable. In this case, we used the power rule for integration to find the antiderivative of $3x^2$.

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