How do you evaluate the definite integral #int 2e^x dx# from #[0,1]#?

Answer 1

The answer is #=2(e-1)#

We use #inte^xdx=e^x+C#
#e^0=1#

Therefore,

#int_0^1 2e^xdx=[2e^x]_0^1#
#=(2e^1-2e^0)#
#=2e-2#
#=2(e-1)#
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Answer 2

To evaluate the definite integral ( \int_{0}^{1} 2e^x , dx ), you can follow these steps:

  1. Integrate the function ( 2e^x ) with respect to ( x ) to find the antiderivative.
  2. Evaluate the antiderivative at the upper limit (1) and subtract the value of the antiderivative at the lower limit (0).

Here's the calculation:

  1. The antiderivative of ( 2e^x ) with respect to ( x ) is ( 2e^x ).
  2. Evaluate ( 2e^x ) at the upper limit (1): ( 2e^1 = 2e ).
  3. Evaluate ( 2e^x ) at the lower limit (0): ( 2e^0 = 2 ).
  4. Subtract the value at the lower limit from the value at the upper limit: ( 2e - 2 ).

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

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Answer from HIX Tutor

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.

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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