What is the integral from 0 to 2 of 3^{2x} ?

The integral from 0 to 2 of 3^{2x} is (40)/(ln(3))

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integral from 0 to 2 of 3^{2x}

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

\frac{40}{ln ( 3 )}

Decimal

36.40956 \dots

Solution steps

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

Simplify

3^{2 x} : 9^{x}

= \int_{0}^{2} 9^{x} d x

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

= [\frac{9 ^{x}}{ln ( 9 )}]_{0}^{2}

Simplify

ln (9) : 2 ln (3)

= [\frac{9 ^{x}}{2 ln ( 3 )}]_{0}^{2}

Compute the boundaries:

\frac{40}{ln ( 3 )}

= \frac{40}{ln ( 3 )}

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What is the integral from 0 to 2 of 3^{2x} ?
The integral from 0 to 2 of 3^{2x} is (40)/(ln(3))