# How do you evaluate the definite integral #int 2^x dx# from #[-1,1]#?

so remembering integration is the reverse of differentiating.

insert the limits and evaluate immediately.

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To evaluate the definite integral ∫2^x dx from -1 to 1, you first need to find the antiderivative of 2^x with respect to x. The antiderivative of 2^x is (1/ln(2)) * 2^x. Then, you evaluate this antiderivative at the upper and lower bounds of integration (-1 and 1) and subtract the value at the lower bound from the value at the upper bound.

So, ∫2^x dx from -1 to 1 = [(1/ln(2)) * 2^x] evaluated from -1 to 1 = [(1/ln(2)) * 2^1] - [(1/ln(2)) * 2^(-1)] = (2/ln(2)) - (1/2ln(2))

Therefore, the value of the definite integral is (2/ln(2)) - (1/2ln(2)).

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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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