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Find the Area Bounded by the Curve Y = E−X, the X-axis and the Y-axis. - Physics

Sum

Find the area bounded by the curve y = ex, the X-axis and the Y-axis.

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Solution

The given function is y = ex.
When x = 0, y = e−0 = 1
When x increases, the value of y decrease. Also, only when x = ∞, = 0

So, the required area can be determined by integrating the function from 0 to ∞.
\[\therefore Area = \int_0^\infty e^{- x} dx\]
\[ = - \left[ e^{- x} \right]_0^\infty \]
\[ = - \left[ 0 - 1 \right] = 1 \text{sq . unit}\]

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APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 2 Physics and Mathematics
Exercise | Q 26 | Page 30
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