What is the integral from-2 to 0 of 4-2^{-x} ?

The integral from-2 to 0 of 4-2^{-x} is 8-3/(ln(2))

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integral from-2 to 0 of 4-2^{-x}

\int_{- 2}^{0} 4 - 2^{- x} d x

8 - \frac{3}{ln ( 2 )}

Decimal Notation

3.67191 \dots

Solution steps

\int_{- 2}^{0} 4 - 2^{- x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- 2}^{0} 4 d x - \int_{- 2}^{0} 2^{- x} d x

\int_{- 2}^{0} 4 d x = 8

\int_{- 2}^{0} 2^{- x} d x = \frac{3}{ln ( 2 )}

= 8 - \frac{3}{ln ( 2 )}

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What is the integral from-2 to 0 of 4-2^{-x} ?
The integral from-2 to 0 of 4-2^{-x} is 8-3/(ln(2))