IIT JEE , AIEEE Forum - Physics , Mechanics

shinee

find the area bonded by the curve y=e^-x, the x axis and the y axis

gunshot

give the limits--

Aatish

hey buddy.......

y = e^-x
for x = 0.......y = 1........so curve cuts y - axis at (0,1)

but when y = 0........x = infinity........so curve does not cuts x-axis..........

and so according to me area under the given curves must be infinity...or not defined........

hash_include

No, the sum is perfectly right. since it cuts the y axis at 1 and x axis at $\infty$ , the limits are from 0 to $\infty$
$\int_0^{\infty} e^{-x} dx = [-e^{-x}]_0^{\infty}$

$=1$
Smile

shinee

hash, 10q v much
can u also please tell me y u have integrated e to the power -x to find the area

shinee

hash, 10q v much
can u also please tell me y u have integrated e to the power -x to find the area

hash_include

well, thats the general rule to find area of a curve been 2 points .
suppose there is a function f(x) and you want to find area under the curve between 2 points a and b on the curve f(x), then
Area = _[a]

^[b] f(x).dx
since you've asked area under e^-xgraph, i'e used e^-x

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