Question

Calculate the area under the curve f(x) = e^-x bounded by the positive x and y axes.

Answer:

The area is 1 square units.

We have to calculate area under the curve bounded by the positive x and y axes.
So, x varies from 0 to ∞.
Therefore, we have to find ∫e^-xdx when x varies from 0 to ∞.
To find the integral of e^-x, we find a function whose derivative is e^-x. Thus, we get ∫e^-xdx = -e^-x.
Therefore, the area under the curve
= -e^-∞ - (-e⁰)
= 0 + 1
= 1 sq. unit


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