IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

srujana

Find the area bounded by the curve y=e^-x , the X axis and the Y axis.

nivedh_89

r u sure it meets both the axes ..... please check n reply................

karthik2007

The area in the first quadrant of y=e^-x is:

The curve touches the axes at 0,

.

So, the integral becomes : _{[0 ]}

^{[infinity ]} e^-xdx = -e^-x] from 0 to infinity, substituting the limits, we get the area as 1 unit.

titun

The graph of the function e ^{- x}is attached with the answer. As, the question wants the area of e ^{- x}with X axis and Y axis, it can mean two areas --- the area in the first quadrant and the area in the second quadrant.

Area in the first quadrant = _{[a ]}

_{[ + infinity ]} _{[ 0 ]}

^[a] e ^{- x}dx = 1 sq. units.

Area in the second quadrant = _{[b ]}

_{[ - infinity ]} _{[ b]}

^{0[ ]} e ^{- x} dx =

Remark : Well, obviously, you can conclude from the graph that the area in the 1st quadrant will have finite value as the curve tends to zero as x tends to

, and hence tends to a closed bounded figure. On the contrary, the area in the second quadrant has infinite value as the curve tends to

as x tends to -

and hence has an open unbounded figure.

Hope that satisfies and resolves all query.

Cheers !!!!!

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