What is the integral from 0 to 2 of (2^x+6) ?

The integral from 0 to 2 of (2^x+6) is 3/(ln(2))+12

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integral from 0 to 2 of (2^x+6)

\int_{0}^{2} (2^{x} + 6) d x

\frac{3}{ln ( 2 )} + 12

Decimal Notation

16.32808 \dots

Solution steps

\int_{0}^{2} 2^{x} + 6 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} 6 d x

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

\int_{0}^{2} 6 d x = 12

= \frac{3}{ln ( 2 )} + 12

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What is the integral from 0 to 2 of (2^x+6) ?
The integral from 0 to 2 of (2^x+6) is 3/(ln(2))+12