# How do you evaluate the definite integral #int2xdx# from #[0,1]#?

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To evaluate the definite integral ( \int_{0}^{1} 2x , dx ), you need to find the antiderivative of ( 2x ) with respect to ( x ), then evaluate it at the upper and lower limits of integration and subtract.

The antiderivative of ( 2x ) with respect to ( x ) is ( x^2 ).

Now, plug in the upper and lower limits of integration into the antiderivative:

[ \int_{0}^{1} 2x , dx = \left[ x^2 \right]_{0}^{1} ]

[ = (1)^2 - (0)^2 ]

[ = 1 - 0 ]

[ = 1 ]

So, the value of the definite integral ( \int_{0}^{1} 2x , dx ) is 1.

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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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