# How do you evaluate the definite integral #intte^(-t)dt# from #[0,6]#?

The answer is

We use integration by parts

Therefore,

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To evaluate the definite integral ∫₀⁶ e^(-t) dt, we use the antiderivative of e^(-t), which is -e^(-t). Then, we substitute the upper and lower limits of integration into this antiderivative and subtract the result evaluated at the lower limit from the result evaluated at the upper limit.

So, ∫₀⁶ e^(-t) dt = -e^(-6) - (-e^(-0)) = -e^(-6) + e^0 = -e^(-6) + 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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