What is the integral from-2 to 2 of 81^{x/2} ?

The integral from-2 to 2 of 81^{x/2} is (3280)/(81ln(3))

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integral from-2 to 2 of 81^{x/2}

\int_{- 2}^{2} 8 1^{\frac{x}{2}} d x

\frac{3280}{81 ln ( 3 )}

Decimal Notation

36.85906 \dots

Solution steps

\int_{- 2}^{2} 8 1^{\frac{x}{2}} d x

Simplify

8 1^{\frac{x}{2}} : 9^{x}

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

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

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

Simplify

ln (9) : 2 ln (3)

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

Compute the boundaries:

\frac{3280}{81 ln ( 3 )}

= \frac{3280}{81 ln ( 3 )}

\frac{( x + 3 )}{( x - 3 )}

9 y^{^{''}} - y = x e^{\frac{x}{3}}, y (0) = 1, y^{^{'}} (0) = 0

\frac{\partial}{\partial y} (\frac{y}{x} + 4 x)

What is the integral from-2 to 2 of 81^{x/2} ?
The integral from-2 to 2 of 81^{x/2} is (3280)/(81ln(3))