# How do you use limits to evaluate #int(x^5+x^2)dx# from [0,2]?

Please see the explanation section below.

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To evaluate the integral ∫(x^5 + x^2) dx from 0 to 2 using limits, you can follow these steps:

- Find the antiderivative of the function, which is (1/6)x^6 + (1/3)x^3.
- Evaluate the antiderivative at the upper limit (2) and subtract the value obtained by evaluating it at the lower limit (0).
- Plug in the upper limit (2) into the antiderivative: (1/6)(2^6) + (1/3)(2^3).
- Plug in the lower limit (0) into the antiderivative: (1/6)(0^6) + (1/3)(0^3).
- Subtract the result obtained in step 4 from the result obtained in step 3.

After calculation, you will find that the integral evaluates to (1/6)(2^6) + (1/3)(2^3) - (1/6)(0^6) - (1/3)(0^3) = (64/3) units.

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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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