1-4-e-x-dx-

Question Number 83145 by 09658867628 last updated on 28/Feb/20

\underset{1}{\int^{4}} e^{\sqrt{x}} d x =

Commented by mathmax by abdo last updated on 28/Feb/20

I = \int_{1}^{4} e^{\sqrt{x}} d x c h a n g e m e n t \sqrt{x} = t g i v e

I = \int_{1}^{2} e^{t} (2 t) d t = 2 \int_{1}^{2} t e^{t} d t =_{b y p a r t s} 2 {{[{t e}^{t}]}_{1}^{2} - \int_{1}^{2} e^{t} d t}

= 2 {2 e^{2} - e - (e^{2} - e)} = 2 {e^{2}} \Rightarrow I = 2 e^{2}

Answered by Kunal12588 last updated on 28/Feb/20

\sqrt{x} = t

d x = 2 t d t

I = 2 \int_{1}^{2} {t e}^{t} d t = 2 {{[{t e}^{t}]}_{1}^{2} - \int_{1}^{2} e^{t} d t}

\Rightarrow I = 2 {2 e^{2} - e - {[e^{t}]}_{1}^{2}}

\Rightarrow I = 2 {2 e^{2} - e - e^{2} + e}

\Rightarrow I = 2 e^{2}

\underset{1}{\int^{4}} e^{\sqrt{x}} d x = 2 e^{2}; i h o p e t h i s i s c o r r e c t