What is the integral from 0 to 1 of 100^x ?

The integral from 0 to 1 of 100^x is (99)/(2ln(10))

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integral from 0 to 1 of 100^x

\int_{0}^{1} 10 0^{x} d x

\frac{99}{2 ln ( 10 )}

Decimal

21.49757 \dots

Solution steps

\int_{0}^{1} 10 0^{x} d x

\int a^{x} d x = \frac{a ^{x}}{ln a}

= [\frac{10 0 ^{x}}{ln ( 100 )}]_{0}^{1}

\frac{10 0 ^{x}}{ln ( 100 )} = \frac{2 5 ^{x} \cdot 2 ^{2 x - 1}}{ln ( 10 )}

= [\frac{2 5 ^{x} \cdot 2 ^{2 x - 1}}{ln ( 10 )}]_{0}^{1}

Compute the boundaries:

\frac{99}{2 ln ( 10 )}

= \frac{99}{2 ln ( 10 )}

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What is the integral from 0 to 1 of 100^x ?
The integral from 0 to 1 of 100^x is (99)/(2ln(10))