What is the integral from 0 to 2 of 2^x-1-(3x)/2 ?

The integral from 0 to 2 of 2^x-1-(3x)/2 is 3/(ln(2))-5

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integral from 0 to 2 of 2^x-1-(3x)/2

\int_{0}^{2} 2^{x} - 1 - \frac{3 x}{2} d x

\frac{3}{ln ( 2 )} - 5

Decimal

- 0.67191 \dots

Solution steps

\int_{0}^{2} 2^{x} - 1 - \frac{3 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} 2^{x} d x - \int_{0}^{2} 1 d x - \int_{0}^{2} \frac{3 x}{2} d x

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

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

\int_{0}^{2} \frac{3 x}{2} d x = 3

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

Simplify

= \frac{3}{ln ( 2 )} - 5

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What is the integral from 0 to 2 of 2^x-1-(3x)/2 ?
The integral from 0 to 2 of 2^x-1-(3x)/2 is 3/(ln(2))-5