# How do you find the lengths of the curve #y=intsqrt(t^2+2t)dt# from [0,x] for the interval #0<=x<=10#?

The solution to this integration already posted elsewhere in tutor.hix, so there is no point of repeating it here.

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To find the length of the curve described by the integral (\int_0^x \sqrt{t^2 + 2t} , dt) for (0 \leq x \leq 10), you would need to evaluate the integral from 0 to x and then substitute the upper limit x into the result.

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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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