=∫^3_23^xdx #160; [We know ∫ a^xdx=axln a+c ] =∫^3_23xln 3 =1ln 3 ^3_2[ 3x]=1ln 3[3^3 3^2]=27 9ln 3 =18ln 3 . ...

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Property 2

Evaluate: ∫...

Question

Evaluate: $3 \int 2 3^{x} d x$

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Solution

$= \int_{2}^{3} 3^{x} d x$ [We know $\int a^{x} d x = \frac{a x}{l n a} + c$ ]
$= \int_{2}^{3} \frac{3 x}{l n 3}$
$= \frac{1}{l n 3}$ $_{2}^{3} [3 x] = \frac{1}{l n 3} [3^{3} - 3^{2}] = \frac{27 - 9}{l n 3}$
$= \frac{18}{l n 3}$ .

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