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Find the antiderivative of

f(x) = 3x^2

May 7, 2024

Find the antiderivative of

f(x) = 3x^2

Generated Graph

Solution by Steps

step 1

To find the antiderivative of

f(x) = 3x^2

, we integrate the function with respect to

x

step 2

The integral of

3x^2

with respect to

x

\int 3x^2 \, dx

step 3

Applying the power rule for integration, which states that

\int x^n \, dx = \frac{x^{n+1}}{n+1} + C

for any real number

n \neq -1

, we get

\int 3x^2 \, dx = 3 \cdot \frac{x^{2+1}}{2+1} + C

step 4

Simplifying the expression, we have

3 \cdot \frac{x^3}{3} + C

step 5

The constant multiples can be cancelled out, resulting in

x^3 + C

Answer

The antiderivative of

f(x) = 3x^2

x^3 + C

Key Concept

Power Rule for Integration

Explanation

The power rule for integration is used to find the antiderivative of a function of the form

x^n

, resulting in

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

when

n \neq -1