primitivas

por *bebelo34 Dom 08 Mar 2015, 02:01

1) Determine y = f (x),x ∈ ℝ , tal que f'(x) = 2f(x) e f(0) = 1

por Man Utd Dom 08 Mar 2015, 04:34

$\\\\ f^{\prime}(x)=2 f(x) \\\\\\ \dfrac{d f(x)}{dx}=2 f(x) \\\\\\ d f(x)=2 \; dx \\\\\\ \int \; \frac{df(x)}{f(x)}=\int \; 2 \; dx \\\\\\ \ln f(x)=2x+C$

$\\\\\\ f(x)=e^{2x+C} \\\\\\ f(x)=e^{2x}e^{C} \\\\\\ f(x)=e^{2x}C$

como f(0)=1 :

$\\\\\\ f(0)=e^{2*0}C \;\; \to \;\; C=1$

logo :

$\\\\\\ f(x)=e^{2x}$

primitivas

primitivas

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