Question

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

Answer 1

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

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