What is the integral from 0 to 2 of 4*2^{-x}-1 ?

The integral from 0 to 2 of 4*2^{-x}-1 is 3/(ln(2))-2

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integral from 0 to 2 of 4*2^{-x}-1

\int_{0}^{2} 4 \cdot 2^{- x} - 1 d x

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

Decimal

2.32808 \dots

Solution steps

\int_{0}^{2} 4 \cdot 2^{- x} - 1 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} 4 \cdot 2^{- x} d x - \int_{0}^{2} 1 d x

\int_{0}^{2} 4 \cdot 2^{- x} d x = \frac{3}{ln ( 2 )}

\int_{0}^{2} 1 d x = 2

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

What is the integral from 0 to 2 of 4*2^{-x}-1 ?
The integral from 0 to 2 of 4*2^{-x}-1 is 3/(ln(2))-2