# How do you find the antiderivative of #f(x)=x^6#?

where c is the constant of integration.

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Antiderivitive means integration:

using the power rule for integration:

This is the final answer:

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To find the antiderivative of ( f(x) = x^6 ), you can use the power rule for integration. The power rule states that the antiderivative of ( x^n ) with respect to ( x ) is ( \frac{x^{n+1}}{n+1} + C ), where ( C ) is the constant of integration. Applying the power rule to ( f(x) = x^6 ), we get:

[ \int x^6 , dx = \frac{x^{6+1}}{6+1} + C = \frac{x^7}{7} + C ]

So, the antiderivative of ( f(x) = x^6 ) is ( \frac{x^7}{7} + C ), where ( C ) is the constant of integration.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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