What is the integral from 0 to 2 of 8*2^{-x}-2 ?

The integral from 0 to 2 of 8*2^{-x}-2 is 6/(ln(2))-4

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integral from 0 to 2 of 8*2^{-x}-2

\int_{0}^{2} 8 \cdot 2^{- x} - 2 d x

\frac{6}{ln ( 2 )} - 4

Decimal

4.65617 \dots

Solution steps

\int_{0}^{2} 8 \cdot 2^{- x} - 2 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_{0}^{2} 8 \cdot 2^{- x} d x - \int_{0}^{2} 2 d x

\int_{0}^{2} 8 \cdot 2^{- x} d x = \frac{6}{ln ( 2 )}

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

= \frac{6}{ln ( 2 )} - 4

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What is the integral from 0 to 2 of 8*2^{-x}-2 ?
The integral from 0 to 2 of 8*2^{-x}-2 is 6/(ln(2))-4