# How do you evaluate the definite integral #int (14x^6)dx# from [-2,2]?

Evaluate the upper and lower limits and subtract upper - lower

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To evaluate the definite integral of ( \int_{-2}^{2} 14x^6 , dx ), you first need to find the antiderivative of ( 14x^6 ) with respect to ( x ), which is ( \frac{14}{7}x^7 ).

Then, apply the fundamental theorem of calculus, which states that the definite integral of a function over an interval is equal to the difference of its antiderivative evaluated at the endpoints of the interval.

So, ( \int_{-2}^{2} 14x^6 , dx = \frac{14}{7}x^7 \Big|_{-2}^{2} ).

Evaluate this expression at ( x = 2 ) and ( x = -2 ) and subtract the result:

( \left( \frac{14}{7}(2)^7 \right) - \left( \frac{14}{7}(-2)^7 \right) ).

Simplify to get your final answer.

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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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