Mathematics

# Solve :- $\displaystyle \int_0^1 \ 3^x dx$

##### SOLUTION
$3 = \ e^{ \ln3}$
$\implies 3^x = e^{\ x\ln3}$

$\therefore \displaystyle\int_0^13^xdx = \displaystyle\int_0^1e^{x\ln3}dx$

$=\dfrac{1}{\ln3}[e^{x\ln3}]_0^1=\dfrac{1}{\ln3}[e^{\ln3}-1]$

$=\dfrac{3-1}{\ln3}$

$=\boxed{\dfrac{2}{\ln3}}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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