calculate-0-1-dx-3-2-x-

Question Number 64159 by mathmax by abdo last updated on 14/Jul/19

c a l c u l a t e \int_{0}^{1} \frac{d x}{3 + 2^{x}}

Commented by turbo msup by abdo last updated on 15/Jul/19

c h s n g e m e n t 2^{x} = t g i v e e^{x l n (2)} = t \Rightarrow

x l n (2) = l n (t) \Rightarrow x = \frac{l n (t)}{l n 2}

\int_{0}^{1} \frac{d x}{3 + 2^{x}} = \int_{1}^{2} \frac{d t}{t l n 2 (3 + t)}

= \frac{1}{3 l n 2} \int_{1}^{2} (\frac{1}{t} - \frac{1}{3 + t}) d t

= \frac{1}{3 l n 2} {[l n (\frac{t}{t + 3})]}_{1}^{2}

= \frac{1}{3 l n 2} {l n (\frac{2}{5}) - l n (\frac{1}{4})}

= \frac{1}{3 l n 2} {l n 2 - l n 5 + 2 l n 2}

= \frac{1}{3 l n 2} {3 l n 2 - l n 5}

Answered by Hope last updated on 15/Jul/19

f (x) = \frac{1}{3 + 2^{x}}

f (0) = \frac{1}{4} = 0.25

f (1) = \frac{1}{5} = 0.2

\int_{0}^{1} f (x) d x = \frac{1}{2} (0.25 + 0.20) \times 1 = 0.225 (a p p r o x)

T a n m a y i s h o p e \dots

Commented by Hope last updated on 15/Jul/19

s t i l l h o p e p r e s e n t . . i h a v e c h a n g e d m y p r o f i l e n a m e

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s o i t r i e d t o m i n i m i s e m y a c t i v i t y i n t h i s

p l a t f o r m . . 0 k g o o d b y e

Commented by mathmax by abdo last updated on 15/Jul/19

s i r t a n m a y y o u a r e w r o n g i f y o u s a y t h i s w h a t s y o u r p r o o f

t h a t y o u r a n s w e r i s n o t a c c e p t e d y o u a r e a l w a y s a c t i f i n t h a t

f o r u m a n d c o n s i d e r e d \dots .