What is the integral from 0 to 1 of (7x-7^x) ?

The integral from 0 to 1 of (7x-7^x) is 7/2-6/(ln(7))

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integral from 0 to 1 of (7x-7^x)

\int_{0}^{1} (7 x - 7^{x}) d x

\frac{7}{2} - \frac{6}{ln ( 7 )}

Decimal

0.41660 \dots

Solution steps

\int_{0}^{1} 7 x - 7^{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_{0}^{1} 7 x d x - \int_{0}^{1} 7^{x} d x

\int_{0}^{1} 7 x d x = \frac{7}{2}

\int_{0}^{1} 7^{x} d x = \frac{6}{ln ( 7 )}

= \frac{7}{2} - \frac{6}{ln ( 7 )}

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What is the integral from 0 to 1 of (7x-7^x) ?
The integral from 0 to 1 of (7x-7^x) is 7/2-6/(ln(7))