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

The answer is

Therefore,

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

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

Here's the calculation:

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