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Math Analysis issue

Maryanne
Visitor

2016-08-25 07:27:11

let be the function f:R->R, f(x) = e^x (x-1).

a) Show that
$int_{0}^{2}f(x)e^{-x} mathrm{d}x= 0$ .

b) Prove that area delimited by the graph of f, the Ox, axis and the lines of equations x = 1 and x = 2 has area equal with e.

RE: Math Analysis issue

Steve McLoud
Visitor

2016-08-25 07:58:52

$math analysis$

$= \int_{0}^{2}(x-1)dx = \left.\begin{matrix} \left ( \frac{x^{2}}{2}-x \right ) \end{matrix}\right|_{0}^{2} = (\frac{4}{2}-2)-0 = 2-2=0$

RE: Math Analysis issue

SteveC
Member

2016-09-08 14:55:59

For the second issue we have:
$S=Int01$

and we use part integration:
$parts integration$

RE: Math Analysis issue

SteveC
Member

2016-09-08 14:59:46

$=e$

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