# How do you find the definite integral for: #xdx# for the intervals #[12, 14]#?

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To find the definite integral of x dx for the intervals [12, 14], you evaluate the antiderivative of x, which is (1/2)x^2. Then, you subtract the value of the antiderivative at the lower limit from the value at the upper limit.

So, the definite integral is:

[ (1/2) * 14^2 ] - [ (1/2) * 12^2 ]

= (1/2) * (14^2 - 12^2)

= (1/2) * (196 - 144)

= (1/2) * 52

= 26.

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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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